Edit Profile (opens in new tab) Klimyk, Anatoliy Ul’yanovich Compute Distance To: Compute Author ID: klimyk.anatoliy-u Published as: Klimyk, A. U.; Klimyk, Anatoli U.; Klimyk, Anatoliy U.; Klimyk, Anatoliy; Klimyk, A.; Klimyk, Anatoli; Klimik, A. U.; Klimyk, Alessio U. more...less Further Spellings: Климык Анатолий Ульянович External Links: Math-Net.Ru · dblp Documents Indexed: 153 Publications since 1966, including 10 Books Reviewing Activity: 154 Reviews Co-Authors: 31 Co-Authors with 104 Joint Publications 522 Co-Co-Authors all top 5 Co-Authors 49 single-authored 15 Atakishiev, Natig M. 13 Kachurik, Ivan I. 11 Gavrilik, Alexandre M. 11 Havlíček, Miloslav 10 Vilenkin, Naum Yakovlevich 8 Iorgov, N. Z. 8 Pošta, Severin 7 Gruber, Bruno J. 7 Patera, Jiří 5 Groza, Valentyna A. 4 Atakishiyev, M. N. 3 Burban, Ivan M. 3 Pelantová, Edita 3 Shirokov, V. A. 2 Kachuryk, Ivan I. 2 Pakuliak, Stanislav Z. 2 Wolf, Kurt Bernardo 1 Chung, Won-Sang 1 Gavrilik, O. M. 1 Golod, P. I. 1 Holod, Petro I. 1 Iorgov, Nikolai 1 Karpelevich, Friedrich I. 1 Koganov, Leonid M. 1 Olshanetsky, Mikhail A. 1 Rogov, V.-B. K. 1 Rubinstein, Aleksandr Iosifovich 1 Santilli, Ruggero Maria 1 Schempp, Walter Johannes 1 Schmüdgen, Konrad 1 Smorodinskij, Ya. A. all top 5 Serials 25 Journal of Mathematical Physics 16 Journal of Physics A: Mathematical and General 10 Dopovidi Akademiï Nauk Ukraïns’koï RSR. Seriya A 7 Czechoslovak Journal of Physics 5 Doklady Akademii Nauk Ukrainskoĭ SSR, Seriya A 5 Letters in Mathematical Physics 5 Ukrainian Mathematical Journal 5 Methods of Functional Analysis and Topology 5 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 4 Ukraïns’kyĭ Matematychnyĭ Zhurnal 4 Journal of Physics A: Mathematical and Theoretical 3 Reports on Mathematical Physics 3 Mathematics and Its Applications. Soviet Series 2 Modern Physics Letters A 2 Journal of Mathematical Analysis and Applications 2 Mathematical Notes 2 Matematicheskie Zametki 2 Teoreticheskaya i Matematicheskaya Fizika 2 Algebras, Groups and Geometries 2 Translations. Series 2. American Mathematical Society 1 Communications in Mathematical Physics 1 Physics Letters. A 1 Russian Mathematical Surveys 1 Theoretical and Mathematical Physics 1 Hadronic Journal 1 International Journal of Mathematics and Mathematical Sciences 1 Soviet Mathematics. Doklady 1 Acta Applicandae Mathematicae 1 CWI Quarterly 1 Atti della Accademia Nazionale dei Lincei. Serie Ottava. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali 1 Dopovidi Akademiï Nauk Ukraïni 1 Integral Transforms and Special Functions 1 Algebras and Representation Theory 1 Dopovidi Natsional’noï Akademiï Nauk Ukraïny. Matematyka, Pryrodoznavstvo, Tekhnichni Nauky 1 Naukovi Zapysky (Kyïv) 1 Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Fundamental’nye Napravleniya 1 Mathematics and its Applications (Dordrecht) 1 Texts and Monographs in Physics all top 5 Fields 78 Nonassociative rings and algebras (17-XX) 74 Quantum theory (81-XX) 59 Topological groups, Lie groups (22-XX) 45 Special functions (33-XX) 14 Abstract harmonic analysis (43-XX) 10 Group theory and generalizations (20-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 6 Associative rings and algebras (16-XX) 6 Difference and functional equations (39-XX) 6 Functional analysis (46-XX) 6 Operator theory (47-XX) 2 Number theory (11-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Relativity and gravitational theory (83-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Partial differential equations (35-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Numerical analysis (65-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 88 Publications have been cited 1,019 times in 830 Documents Cited by ▼ Year ▼ Quantum groups and their representations. Zbl 0891.17010Klimyk, Anatoli; Schmüdgen, Konrad 278 1997 Representation of Lie groups and special functions. Volume 1: Simplest Lie groups, special functions and integral transforms. Transl. from the Russian by V. A. Groza and A. A. Groza. Zbl 0742.22001Vilenkin, N. Ya.; Klimyk, A. U. 91 1991 Representation of Lie groups and special functions. Volume 2: Class I representations, special functions, and integral transforms. Zbl 0809.22001Vilenkin, N. Ya.; Klimyk, A. U. 60 1993 Representation of Lie groups and special functions. Recent advances. Transl. from the Russian by V. A. Groza a. A. A. Groza. Zbl 0826.22001Vilenkin, N. Ja.; Klimyk, A. U. 47 1994 \(P,Q\)-differentiation, \(P,Q\)-integration, and \(P,Q\)-hypergeometric functions related to quantum groups. Zbl 0823.33010Burban, Ivan M.; Klimyk, Anatoli U. 46 1994 Representation of Lie groups and special functions. Volume 3: Classical and quantum groups and special functions. Transl. from the Russian by V. A. Groza and A. A. Groza. Zbl 0778.22001Vilenkin, N. Ya.; Klimyk, A. U. 38 1992 \(q\)-deformed orthogonal and pseudo-orthogonal algebras and their representations. Zbl 0735.17020Gavrilik, A. M.; Klimyk, A. U. 32 1991 Orbit functions. Zbl 1118.33004Klimyk, Anatoliy; Patera, Jiri 22 2006 Representations of the quantum algebra \(U_ q(su_{1,1})\). Zbl 0780.17010Burban, I. M.; Klimyk, A. U. 21 1993 Representation matrix elements and Clebsch-Gordan coefficients of the semisimple Lie groups. Zbl 0416.22017Klimyk, A. U.; Gavrilik, A. M. 20 1979 On Clebsch-Gordan coefficients and matrix elements of representations of the quantum algebra \(U_ q(su_ 2)\). Zbl 0735.17021Groza, V. A.; Kachurik, I. I.; Klimyk, A. U. 18 1990 Antisymmetric orbit functions. Zbl 1138.33001Klimyk, Anatoliy; Patera, Jiri 16 2007 Representations of the cyclically symmetric \(q\)-deformed algebra \(\text{so}_q(3)\). Zbl 0959.17015Havlíček, M.; Klimyk, A. U.; Pošta, S. 15 1999 General recurrence relations for Clebsch-Gordan coefficients of the quantum algebra \(U_ q(su_ 2)\). Zbl 0742.33014Kachurik, I. I.; Klimyk, A. U. 14 1991 Matrix elements and the Clebsch-Gordan coefficients of groups representations. (Matricnye elementy i koefficienty Klebsa-Gordana predstavlenii grupp.). Zbl 0412.22004Klimyk, A. U. 12 1979 Classification theorem on irreducible representations of the \(q\)-deformed algebra \(U_q^{\prime}(\text{so}_n)\). Zbl 1127.17016Iorgov, N. Z.; Klimyk, A. U. 12 2005 Decomposition of a direct product of irreducible representations of a semisimple Lie algebra into a direct sum of irreducible representations. Zbl 0228.17004Klimyk, A. U. 11 1966 (Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms. Zbl 1152.81513Klimyk, A.; Patera, J. 11 2007 (Anti)symmetric multivariate exponential functions and corresponding Fourier transforms. Zbl 1139.42001Klimyk, A. U.; Patera, J. 10 2007 Infinitesimal operators for representations of complex Lie groups and Clebsch-Gordan coefficients for compact groups. Zbl 0497.22016Klimyk, A. U. 10 1982 On spectral properties of \(q\)-oscillator operators. Zbl 0789.17007Burban, I. M.; Klimyk, A. U. 9 1993 Matrix elements for infinitesimal operators of the groups \(U(p+q)\) and \(U(p,q)\) in a \(U(p)\times U(q)\) basis. I. Zbl 0427.22016Klimyk, Anatoli U.; Gruber, Bruno 9 1979 Representations of Lie groups and special functions. Zbl 0818.22008Klimyk, A. U.; Vilenkin, N. Ya. 8 1990 \(E\)-orbit functions. Zbl 1139.33001Klimyk, Anatoliy U.; Patera, Jiri 8 2008 Structure and matrix elements of the degenerate series representations of \(U(p+q)\) and U(p,q) in a U(p)\(\times U(q)\) basis. Zbl 0548.22011Klimyk, Anatoli U.; Gruber, Bruno 8 1982 The representations of the groups \(U(n,1)\) and \(SO_0(n,1)\). (Predstavlenija grupp \(U(n,1)\) i \(SO_0(n,1)\)). Zbl 0337.22020Klimyk, A. U.; Gavrilik, A. M. 8 1976 Big \(q\)-Laguerre and \(q\)-Meixner polynomials and representations of the quantum algebra \(U_q(su_{1,1}\)). Zbl 1058.81040Atakishiyev, M. N.; Atakishiyev, N. M.; Klimyk, A. U. 7 2003 Representations of the groups Sp(n,R) and Sp(n) in a U(n) basis. Zbl 0548.22010Klimyk, Anatoli U. 7 1983 On position and momentum operators in the \(q\)-oscillator algebra. Zbl 0879.47041Chung, Won-Sang; Klimyk, Anatoli U. 7 1996 On position and momentum operators in the \(q\)-oscillator. Zbl 1067.81060Klimyk, A. U. 6 2005 Wigner-Eckart theorem for the quantum group \(U_ q(n)\). Zbl 0761.17013Klimyk, A. U. 6 1992 On \(q\)-orthogonal polynomials, dual to little and big \(q\)-Jacobi polynomials. Zbl 1049.33013Atakishiyev, N. M.; Klimyk, A. U. 6 2004 Matrix elements for indecomposable representations of complex su(2). Zbl 0548.17005Gruber, Bruno; Klimyk, Anatoli U. 6 1984 On representations of the groups Sp(n,1) and Sp(n). Zbl 0591.22014Holod, P. I.; Klimyk, A. U. 6 1985 Multiplicity free and finite multiplicity indecomposable representations of the algebra su(1,1). Zbl 0425.22023Gruber, Bruno; Klimyk, A. U. 6 1978 Properties of linear representations with a highest weight for the semisimple Lie algebras. Zbl 0308.17002Gruber, B.; Klimyk, A. U. 5 1975 Central elements of the algebras \(U'_q(\text{so}_m)\) and \(U_q(\text{iso}_m)\). Zbl 0977.22005Havlíček, M.; Klimyk, A. U.; Pošta, S. 5 2000 Multiplicities of weights of representations and multiplicities of representations of semisimple Lie algebras. Zbl 0239.17005Klimyk, A. U. 5 1967 On Racah coefficients of the quantum algebra \(U_ q(su_ 2)\). Zbl 0708.17018Kachurik, I. I.; Klimyk, A. U. 5 1990 Representations of Lie groups and special functions. Zbl 0727.22007Vilenkin, N. Ya.; Klimyk, A. U. 5 1990 Classical and quantum Heisenberg groups, their representations and applications. Zbl 0857.22007Klimyk, A. U.; Schempp, W. 4 1996 Representations of the \(q\)-deformed algebras \(U_ q(so_{2,1})\) and \(U_ q(so_{3,1})\). Zbl 0809.17010Gavrilik, A. M.; Klimyk, A. U. 4 1994 Representations of the nonstandard (twisted) deformation \(U'_q(\text{so}_n)\) for \(q\) a root of unity. Zbl 1045.22012Iorgov, N. Z.; Klimyk, A. U. 4 2000 The \(q\)-Laplace operator and \(q\)-harmonic polynomials on the quantum vector space. Zbl 1023.33015Iorgov, N. Z.; Klimyk, A. U. 4 2001 Representations of the groups GL(n,R) and SU(n) in an SO(n) basis. Zbl 0485.22021Gruber, Bruno; Klimyk, Anatoli U. 4 1981 Matrix elements for infinitesimal operators of the groups \(U(p+q)\) and \(U(p,q)\) in a \(U(p)\times U(q)\) basis. II. Zbl 0427.22017Klimyk, A. U. 4 1979 A discrete quantum model of the harmonic oscillator. Zbl 1138.81016Atakishiyev, Natig M.; Klimyk, Anatoliy U.; Wolf, Kurt Bernardo 4 2008 Nonstandard quantization of the enveloping algebra \(U(\text{so}(n))\) and its applications. Zbl 1248.17013Klimyk, A. U. 4 2001 On \(\text{su}_{q}(1,1)\)-models of quantum oscillator. Zbl 1112.81058Atakishiyev, M. N.; Atakishiyev, N. M.; Klimyk, A. U. 4 2006 Nonstandard \(U_q(\text{so}_3)\) and \(U_q(\text{so}_4)\): Tensor products of representations, oscillator realizations and roots of unity. Zbl 0942.17005Havlíček, M.; Pelantová, E.; Klimyk, A. 3 1997 The nonstandard deformation \(U_q'(so_n)\) for \(q\) a root of unity. Zbl 0980.17009Iorgov, N. Z.; Klimyk, A. U. 3 2000 The factorization of a \(q\)-difference equation for continuous \(q\)-Hermite polynomials. Zbl 1120.39015Atakishiyev, M. N.; Klimyk, A. U. 3 2007 Operator spectra for quantum algebras and \(q\)-orthogonal polynomials. Zbl 0833.17012Kachurik, I. I.; Klimyk, A. U. 3 1994 Infinitesimal operators and structure of the most degenerate representations of the groups \(Sp(p+q)\) and Sp(p,q) in an Sp(p)\(\times Sp(q)\) basis. Zbl 0548.22009Klimyk, A. U.; Gruber, Bruno 3 1984 Representations of the \(q\)-deformed algebra \(U_q'(\text{so}_4)\). Zbl 1017.81025Havlíček, M.; Klimyk, A. U.; Pošta, S. 3 2001 Matrix elements of tensor operators. Zbl 0313.22013Klimyk, A. U. 3 1975 On classification of irreducible representations of \(q\)-deformed algebra \(U_q'(\operatorname {so}_3)\) related to quantum gravity. Zbl 1040.81043Klimyk, A. U. 3 2002 On discrete \(q\)-ultraspherical polynomials and their duals. Zbl 1076.33013Atakishiyev, N. M.; Klimyk, A. U. 3 2005 Clebsch-Gordan coefficients for the unitary, orthogonal and symplectic groups and Clebsch-Gordan series for the unitary group. Zbl 0188.29603Klimyk, A. U. 3 1968 Representations of the quantum algebras \(U_{q}(u_{r,s})\) and \(U_{q}(u_{r+s})\) related to the quantum hyperboloid and sphere. Zbl 0767.17011Klimyk, A. U.; Pakuliak, S. Z. 2 1992 Analysis of the representations of the Lorentz and Euclidean groups of \(n\)-th order. (Analiz predstavlenii n-mernyh grupp Lorenca i Evklida.) Preprint. Zbl 0341.20029Gavrilik, A. M.; Klimyk, A. U. 2 1975 Finite \(q\)-oscillator. Zbl 1058.81041Atakishiyev, Natig M.; Klimyk, Anatoliy U.; Wolf, Kurt Bernardo 2 2004 Numerical methods in the theory of group representations. (Vychislitel’nye metody v teorii predstavlenij grupp). Zbl 0649.22011Klimyk, A. U.; Kachurik, I. I. 2 1986 Alternating multivariate trigonometric functions and corresponding Fourier transforms. Zbl 1183.33027Klimyk, A. U.; Patera, J. 2 2008 Representations of the \(q\)-deformed algebra \(U_ q^ \prime ({\mathfrak {so}}_ 4)\). Zbl 0840.17014Kachurik, I. I.; Klimyk, A. U. 2 1994 Spectra, eigenvectors and overlap functions for representation operators of \(q\)-deformed algebras. Zbl 0846.17013Klimyk, A. U.; Kachurik, I. I. 2 1996 Representations of the group SU(1,1) and the Krawtchouk-Meixner functions. Zbl 0645.33020Vilenkin, N. Ya.; Klimyk, A. U. 2 1988 The representation of \(q\)-deformed algebras \(U_ q(so_{3,1})\), \(U_ q(so_ 4)\) and \(q\)-orthogonal polynomials. Zbl 0886.17010Kachurik, I. I.; Klimyk, A. U. 1 1993 \(q\)-deformed Euclidean algebras and their representations. Zbl 0856.17011Groza, V. A.; Kachurik, I. I.; Klimyk, A. U. 1 1995 Standard isorepresentations of isotopic/\(Q\)-operator-deformations of Lie algebras. Zbl 0803.17002Klimyk, Anatoli U.; Santilli, Ruggero M. 1 1993 Symmetries of Clebsch-Gordan coefficients of the quantum group \(U_ q(n)\). Zbl 0832.17014Klimyk, A. U. 1 1995 The embedding \(\text{U}_q^\prime(\text{so}_3)\subset\text{U}_q(\text{sl}_3)\). Zbl 1022.17010Kachurik, I. I.; Klimyk, A. U. 1 2001 Wigner-Eckart theorem and infinitesimal operators of group representations. Zbl 0578.22025Klimyk, A. U. 1 1983 Alternating group and multivariate exponential functions. Zbl 1184.42007Klimyk, Anatoliy; Patera, Jiří 1 2009 Nonclassical type representations of the \(q\)-deformed algebra \(U_q'(\text{so}_n)\). Zbl 0979.17006Iorgov, N. Z.; Klimyk, A. U. 1 2000 On the tensor product of representations of semisimple Lie groups. Zbl 0354.22017Klimyk, A. U. 1 1977 Representation for matrix elements of compact Lie groups. Zbl 0449.22020Klimyk, A. U. 1 1980 Matrix elements of representations of the group ISO(n). Zbl 0489.22014Kachurik, I. I.; Klimyk, A. U. 1 1981 Decomposition of highest-weight representations of a semisimple Lie algebra into representations of regular subalgebras. Zbl 0228.17005Klimyk, A. U. 1 1970 Infinitesimal operators of group representations in noncanonical bases. Zbl 0681.22019Klimyk, A. U.; Kachurik, I. I. 1 1988 On characters of irreducible representations with integer highest weight of a semisimple Lie algebra. Zbl 0184.06003Klimyk, A. U. 1 1968 Decomposition of representations with highest of semisimple Lie algebra into representations of regular subalgebra. Zbl 0196.06202Klimyk, Alessio U. 1 1969 Representations of the quantum algebra \(U_{q,s}({\mathfrak s} {\mathfrak u}_{1,1})\). Zbl 0832.17015Klimyk, A. U. 1 1993 Jacobi matrix pair and dual alternative \(q\)-Charlier polynomials. Zbl 1097.33014Atakishiyev, N. M.; Klimyk, A. U. 1 2005 Spectra of observables in the \(q\)-oscillator and \(q\)-analogue of the Fourier transform. Zbl 1098.81035Klimyk, Anatoliy U. 1 2005 Matrix elements of irreducible representations of the group U(n,1). Zbl 0394.20036Gavrilik, O. M.; Klimik, A. U. 1 1978 Representations of the group Sp(n,1). Zbl 0398.20048Golod, P. I.; Klimik, A. U. 1 1978 Matrix elements and Casimir operators of the discrete series representations of the group U(p,q). Zbl 0418.22018Klimyk, A. U. 1 1979 Alternating group and multivariate exponential functions. Zbl 1184.42007Klimyk, Anatoliy; Patera, Jiří 1 2009 \(E\)-orbit functions. Zbl 1139.33001Klimyk, Anatoliy U.; Patera, Jiri 8 2008 A discrete quantum model of the harmonic oscillator. Zbl 1138.81016Atakishiyev, Natig M.; Klimyk, Anatoliy U.; Wolf, Kurt Bernardo 4 2008 Alternating multivariate trigonometric functions and corresponding Fourier transforms. Zbl 1183.33027Klimyk, A. U.; Patera, J. 2 2008 Antisymmetric orbit functions. Zbl 1138.33001Klimyk, Anatoliy; Patera, Jiri 16 2007 (Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms. Zbl 1152.81513Klimyk, A.; Patera, J. 11 2007 (Anti)symmetric multivariate exponential functions and corresponding Fourier transforms. Zbl 1139.42001Klimyk, A. U.; Patera, J. 10 2007 The factorization of a \(q\)-difference equation for continuous \(q\)-Hermite polynomials. Zbl 1120.39015Atakishiyev, M. N.; Klimyk, A. U. 3 2007 Orbit functions. Zbl 1118.33004Klimyk, Anatoliy; Patera, Jiri 22 2006 On \(\text{su}_{q}(1,1)\)-models of quantum oscillator. Zbl 1112.81058Atakishiyev, M. N.; Atakishiyev, N. M.; Klimyk, A. U. 4 2006 Classification theorem on irreducible representations of the \(q\)-deformed algebra \(U_q^{\prime}(\text{so}_n)\). Zbl 1127.17016Iorgov, N. Z.; Klimyk, A. U. 12 2005 On position and momentum operators in the \(q\)-oscillator. Zbl 1067.81060Klimyk, A. U. 6 2005 On discrete \(q\)-ultraspherical polynomials and their duals. Zbl 1076.33013Atakishiyev, N. M.; Klimyk, A. U. 3 2005 Jacobi matrix pair and dual alternative \(q\)-Charlier polynomials. Zbl 1097.33014Atakishiyev, N. M.; Klimyk, A. U. 1 2005 Spectra of observables in the \(q\)-oscillator and \(q\)-analogue of the Fourier transform. Zbl 1098.81035Klimyk, Anatoliy U. 1 2005 On \(q\)-orthogonal polynomials, dual to little and big \(q\)-Jacobi polynomials. Zbl 1049.33013Atakishiyev, N. M.; Klimyk, A. U. 6 2004 Finite \(q\)-oscillator. Zbl 1058.81041Atakishiyev, Natig M.; Klimyk, Anatoliy U.; Wolf, Kurt Bernardo 2 2004 Big \(q\)-Laguerre and \(q\)-Meixner polynomials and representations of the quantum algebra \(U_q(su_{1,1}\)). Zbl 1058.81040Atakishiyev, M. N.; Atakishiyev, N. M.; Klimyk, A. U. 7 2003 On classification of irreducible representations of \(q\)-deformed algebra \(U_q'(\operatorname {so}_3)\) related to quantum gravity. Zbl 1040.81043Klimyk, A. U. 3 2002 The \(q\)-Laplace operator and \(q\)-harmonic polynomials on the quantum vector space. Zbl 1023.33015Iorgov, N. Z.; Klimyk, A. U. 4 2001 Nonstandard quantization of the enveloping algebra \(U(\text{so}(n))\) and its applications. Zbl 1248.17013Klimyk, A. U. 4 2001 Representations of the \(q\)-deformed algebra \(U_q'(\text{so}_4)\). Zbl 1017.81025Havlíček, M.; Klimyk, A. U.; Pošta, S. 3 2001 The embedding \(\text{U}_q^\prime(\text{so}_3)\subset\text{U}_q(\text{sl}_3)\). Zbl 1022.17010Kachurik, I. I.; Klimyk, A. U. 1 2001 Central elements of the algebras \(U'_q(\text{so}_m)\) and \(U_q(\text{iso}_m)\). Zbl 0977.22005Havlíček, M.; Klimyk, A. U.; Pošta, S. 5 2000 Representations of the nonstandard (twisted) deformation \(U'_q(\text{so}_n)\) for \(q\) a root of unity. Zbl 1045.22012Iorgov, N. Z.; Klimyk, A. U. 4 2000 The nonstandard deformation \(U_q'(so_n)\) for \(q\) a root of unity. Zbl 0980.17009Iorgov, N. Z.; Klimyk, A. U. 3 2000 Nonclassical type representations of the \(q\)-deformed algebra \(U_q'(\text{so}_n)\). Zbl 0979.17006Iorgov, N. Z.; Klimyk, A. U. 1 2000 Representations of the cyclically symmetric \(q\)-deformed algebra \(\text{so}_q(3)\). Zbl 0959.17015Havlíček, M.; Klimyk, A. U.; Pošta, S. 15 1999 Quantum groups and their representations. Zbl 0891.17010Klimyk, Anatoli; Schmüdgen, Konrad 278 1997 Nonstandard \(U_q(\text{so}_3)\) and \(U_q(\text{so}_4)\): Tensor products of representations, oscillator realizations and roots of unity. Zbl 0942.17005Havlíček, M.; Pelantová, E.; Klimyk, A. 3 1997 On position and momentum operators in the \(q\)-oscillator algebra. Zbl 0879.47041Chung, Won-Sang; Klimyk, Anatoli U. 7 1996 Classical and quantum Heisenberg groups, their representations and applications. Zbl 0857.22007Klimyk, A. U.; Schempp, W. 4 1996 Spectra, eigenvectors and overlap functions for representation operators of \(q\)-deformed algebras. Zbl 0846.17013Klimyk, A. U.; Kachurik, I. I. 2 1996 \(q\)-deformed Euclidean algebras and their representations. Zbl 0856.17011Groza, V. A.; Kachurik, I. I.; Klimyk, A. U. 1 1995 Symmetries of Clebsch-Gordan coefficients of the quantum group \(U_ q(n)\). Zbl 0832.17014Klimyk, A. U. 1 1995 Representation of Lie groups and special functions. Recent advances. Transl. from the Russian by V. A. Groza a. A. A. Groza. Zbl 0826.22001Vilenkin, N. Ja.; Klimyk, A. U. 47 1994 \(P,Q\)-differentiation, \(P,Q\)-integration, and \(P,Q\)-hypergeometric functions related to quantum groups. Zbl 0823.33010Burban, Ivan M.; Klimyk, Anatoli U. 46 1994 Representations of the \(q\)-deformed algebras \(U_ q(so_{2,1})\) and \(U_ q(so_{3,1})\). Zbl 0809.17010Gavrilik, A. M.; Klimyk, A. U. 4 1994 Operator spectra for quantum algebras and \(q\)-orthogonal polynomials. Zbl 0833.17012Kachurik, I. I.; Klimyk, A. U. 3 1994 Representations of the \(q\)-deformed algebra \(U_ q^ \prime ({\mathfrak {so}}_ 4)\). Zbl 0840.17014Kachurik, I. I.; Klimyk, A. U. 2 1994 Representation of Lie groups and special functions. Volume 2: Class I representations, special functions, and integral transforms. Zbl 0809.22001Vilenkin, N. Ya.; Klimyk, A. U. 60 1993 Representations of the quantum algebra \(U_ q(su_{1,1})\). Zbl 0780.17010Burban, I. M.; Klimyk, A. U. 21 1993 On spectral properties of \(q\)-oscillator operators. Zbl 0789.17007Burban, I. M.; Klimyk, A. U. 9 1993 The representation of \(q\)-deformed algebras \(U_ q(so_{3,1})\), \(U_ q(so_ 4)\) and \(q\)-orthogonal polynomials. Zbl 0886.17010Kachurik, I. I.; Klimyk, A. U. 1 1993 Standard isorepresentations of isotopic/\(Q\)-operator-deformations of Lie algebras. Zbl 0803.17002Klimyk, Anatoli U.; Santilli, Ruggero M. 1 1993 Representations of the quantum algebra \(U_{q,s}({\mathfrak s} {\mathfrak u}_{1,1})\). Zbl 0832.17015Klimyk, A. U. 1 1993 Representation of Lie groups and special functions. Volume 3: Classical and quantum groups and special functions. Transl. from the Russian by V. A. Groza and A. A. Groza. Zbl 0778.22001Vilenkin, N. Ya.; Klimyk, A. U. 38 1992 Wigner-Eckart theorem for the quantum group \(U_ q(n)\). Zbl 0761.17013Klimyk, A. U. 6 1992 Representations of the quantum algebras \(U_{q}(u_{r,s})\) and \(U_{q}(u_{r+s})\) related to the quantum hyperboloid and sphere. Zbl 0767.17011Klimyk, A. U.; Pakuliak, S. Z. 2 1992 Representation of Lie groups and special functions. Volume 1: Simplest Lie groups, special functions and integral transforms. Transl. from the Russian by V. A. Groza and A. A. Groza. Zbl 0742.22001Vilenkin, N. Ya.; Klimyk, A. U. 91 1991 \(q\)-deformed orthogonal and pseudo-orthogonal algebras and their representations. Zbl 0735.17020Gavrilik, A. M.; Klimyk, A. U. 32 1991 General recurrence relations for Clebsch-Gordan coefficients of the quantum algebra \(U_ q(su_ 2)\). Zbl 0742.33014Kachurik, I. I.; Klimyk, A. U. 14 1991 On Clebsch-Gordan coefficients and matrix elements of representations of the quantum algebra \(U_ q(su_ 2)\). Zbl 0735.17021Groza, V. A.; Kachurik, I. I.; Klimyk, A. U. 18 1990 Representations of Lie groups and special functions. Zbl 0818.22008Klimyk, A. U.; Vilenkin, N. Ya. 8 1990 On Racah coefficients of the quantum algebra \(U_ q(su_ 2)\). Zbl 0708.17018Kachurik, I. I.; Klimyk, A. U. 5 1990 Representations of Lie groups and special functions. Zbl 0727.22007Vilenkin, N. Ya.; Klimyk, A. U. 5 1990 Representations of the group SU(1,1) and the Krawtchouk-Meixner functions. Zbl 0645.33020Vilenkin, N. Ya.; Klimyk, A. U. 2 1988 Infinitesimal operators of group representations in noncanonical bases. Zbl 0681.22019Klimyk, A. U.; Kachurik, I. I. 1 1988 Numerical methods in the theory of group representations. (Vychislitel’nye metody v teorii predstavlenij grupp). Zbl 0649.22011Klimyk, A. U.; Kachurik, I. I. 2 1986 On representations of the groups Sp(n,1) and Sp(n). Zbl 0591.22014Holod, P. I.; Klimyk, A. U. 6 1985 Matrix elements for indecomposable representations of complex su(2). Zbl 0548.17005Gruber, Bruno; Klimyk, Anatoli U. 6 1984 Infinitesimal operators and structure of the most degenerate representations of the groups \(Sp(p+q)\) and Sp(p,q) in an Sp(p)\(\times Sp(q)\) basis. Zbl 0548.22009Klimyk, A. U.; Gruber, Bruno 3 1984 Representations of the groups Sp(n,R) and Sp(n) in a U(n) basis. Zbl 0548.22010Klimyk, Anatoli U. 7 1983 Wigner-Eckart theorem and infinitesimal operators of group representations. Zbl 0578.22025Klimyk, A. U. 1 1983 Infinitesimal operators for representations of complex Lie groups and Clebsch-Gordan coefficients for compact groups. Zbl 0497.22016Klimyk, A. U. 10 1982 Structure and matrix elements of the degenerate series representations of \(U(p+q)\) and U(p,q) in a U(p)\(\times U(q)\) basis. Zbl 0548.22011Klimyk, Anatoli U.; Gruber, Bruno 8 1982 Representations of the groups GL(n,R) and SU(n) in an SO(n) basis. Zbl 0485.22021Gruber, Bruno; Klimyk, Anatoli U. 4 1981 Matrix elements of representations of the group ISO(n). Zbl 0489.22014Kachurik, I. I.; Klimyk, A. U. 1 1981 Representation for matrix elements of compact Lie groups. Zbl 0449.22020Klimyk, A. U. 1 1980 Representation matrix elements and Clebsch-Gordan coefficients of the semisimple Lie groups. Zbl 0416.22017Klimyk, A. U.; Gavrilik, A. M. 20 1979 Matrix elements and the Clebsch-Gordan coefficients of groups representations. (Matricnye elementy i koefficienty Klebsa-Gordana predstavlenii grupp.). Zbl 0412.22004Klimyk, A. U. 12 1979 Matrix elements for infinitesimal operators of the groups \(U(p+q)\) and \(U(p,q)\) in a \(U(p)\times U(q)\) basis. I. Zbl 0427.22016Klimyk, Anatoli U.; Gruber, Bruno 9 1979 Matrix elements for infinitesimal operators of the groups \(U(p+q)\) and \(U(p,q)\) in a \(U(p)\times U(q)\) basis. II. Zbl 0427.22017Klimyk, A. U. 4 1979 Matrix elements and Casimir operators of the discrete series representations of the group U(p,q). Zbl 0418.22018Klimyk, A. U. 1 1979 Multiplicity free and finite multiplicity indecomposable representations of the algebra su(1,1). Zbl 0425.22023Gruber, Bruno; Klimyk, A. U. 6 1978 Matrix elements of irreducible representations of the group U(n,1). Zbl 0394.20036Gavrilik, O. M.; Klimik, A. U. 1 1978 Representations of the group Sp(n,1). Zbl 0398.20048Golod, P. I.; Klimik, A. U. 1 1978 On the tensor product of representations of semisimple Lie groups. Zbl 0354.22017Klimyk, A. U. 1 1977 The representations of the groups \(U(n,1)\) and \(SO_0(n,1)\). (Predstavlenija grupp \(U(n,1)\) i \(SO_0(n,1)\)). Zbl 0337.22020Klimyk, A. U.; Gavrilik, A. M. 8 1976 Properties of linear representations with a highest weight for the semisimple Lie algebras. Zbl 0308.17002Gruber, B.; Klimyk, A. U. 5 1975 Matrix elements of tensor operators. Zbl 0313.22013Klimyk, A. U. 3 1975 Analysis of the representations of the Lorentz and Euclidean groups of \(n\)-th order. (Analiz predstavlenii n-mernyh grupp Lorenca i Evklida.) Preprint. Zbl 0341.20029Gavrilik, A. M.; Klimyk, A. U. 2 1975 Decomposition of highest-weight representations of a semisimple Lie algebra into representations of regular subalgebras. Zbl 0228.17005Klimyk, A. U. 1 1970 Decomposition of representations with highest of semisimple Lie algebra into representations of regular subalgebra. Zbl 0196.06202Klimyk, Alessio U. 1 1969 Clebsch-Gordan coefficients for the unitary, orthogonal and symplectic groups and Clebsch-Gordan series for the unitary group. Zbl 0188.29603Klimyk, A. U. 3 1968 On characters of irreducible representations with integer highest weight of a semisimple Lie algebra. Zbl 0184.06003Klimyk, A. U. 1 1968 Multiplicities of weights of representations and multiplicities of representations of semisimple Lie algebras. Zbl 0239.17005Klimyk, A. U. 5 1967 Decomposition of a direct product of irreducible representations of a semisimple Lie algebra into a direct sum of irreducible representations. Zbl 0228.17004Klimyk, A. U. 11 1966 all cited Publications top 5 cited Publications all top 5 Cited by 961 Authors 38 Klimyk, Anatoliy Ul’yanovich 18 Vinet, Luc 13 Marinucci, Domenico 12 Atakishiev, Natig M. 12 Landi, Giovanni 12 Patera, Jiří 11 Rubin, Boris 10 Fakhri, Hossein 10 Hrivnák, Jiří 9 Koelink, Erik 8 Eelbode, David 8 Genest, Vincent X. 8 Gruber, Bruno J. 8 Kolb, Stefan 8 Van der Jeugt, Joris 7 Chirvăsitu, Alexandru 7 Gavrilik, Alexandre M. 7 Heckenberger, István 7 Hu, Naihong 7 Kachurik, Ivan I. 7 Krähmer, Ulrich 7 Matassa, Marco 6 Acar, Tuncer 6 Bichon, Julien 6 Crampé, Nicolas 6 O’Buachalla, Réamonn 6 Ruzhansky, Michael V. 6 Sahai, Vivek 6 Terwilliger, Paul M. 6 van Diejen, Jan Felipe 6 Zhedanov, Alexei S. 5 Area, Iván 5 Damaskinskij, E. V. 5 De Commer, Kenny 5 Emsiz, Erdal 5 Kaad, Jens 5 Kyed, David 5 Motlochová, Lenka 5 Saurabh, Bipul 5 Sayyah-Fard, M. 5 Schmüdgen, Konrad 5 Szajewska, Marzena 5 Yadav, Sarasvati 4 Ališauskas, Sigitas 4 Aral, Ali 4 Baseilhac, Pascal 4 Choi, Junesang 4 D’Andrea, Francesco 4 Fioresi, Rita 4 Geller, Daryl 4 Hartwig, Jonas T. 4 Havlíček, Miloslav 4 Hounkonnou, Mahouton Norbert 4 Huang, Hau-wen 4 Lowe, David A. 4 Masjed-Jamei, Mohammad 4 Mohiuddine, Syed Abdul 4 Molev, Alexander I. 4 Morozov, Andreĭ Alekseevich 4 Pagani, Chiara 4 Pošta, Severin 4 Ragoucy, Eric 4 Razumov, Alexander V. 4 Roels, Matthias 4 Scarabotti, Fabio 4 Shilin, Il’ya Anatol’evich 4 Sokolov, M. A. 4 Soleyman, Fatemeh 4 Stoilova, Nedjalka I. 3 Aguilar, Konrad 3 Álvarez-Nodarse, Renato 3 Bershtein, Olga 3 Bogolyubov, Nikolaĭ Mikhaĭlovich 3 Cantuba, Rafael Reno S. 3 Çelik, Sultan Abaci 3 Chakraborty, Partha Sarathi 3 Chirikjian, Gregory S. 3 Ciccoli, Nicola 3 Dabrowski, Ludwik 3 De Bie, Hendrik 3 Finkelstein, Robert J. 3 Gaboriaud, Julien 3 Gade, R. M. 3 Geyer, Bodo 3 Gould, Mark D. 3 Hadfield, Tom 3 Hu, Hongmei 3 Jain, Pankaj 3 Kharchenko, Vladislav K. 3 Knapp, Anthony William 3 Koornwinder, Tom H. 3 Kravchuk, Petr 3 Kulish, Petr Petrovich 3 Kumar, Vishvesh 3 Lazar, Markus 3 Lievens, Stijn 3 Man’ko, Vladimir Ivanovich 3 Morozov, Alexei Yurievich 3 Mursaleen, Mohammad 3 Neshveyev, Sergey V. ...and 861 more Authors all top 5 Cited in 203 Serials 113 Journal of Mathematical Physics 46 Journal of Algebra 36 Communications in Mathematical Physics 36 Nuclear Physics. B 25 Letters in Mathematical Physics 24 Theoretical and Mathematical Physics 19 Journal of Geometry and Physics 19 Journal of Functional Analysis 16 Journal of Mathematical Analysis and Applications 16 Advances in Mathematics 16 Journal of High Energy Physics 13 Journal of Pure and Applied Algebra 13 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 12 Journal of Computational and Applied Mathematics 11 Reports on Mathematical Physics 11 Transactions of the American Mathematical Society 11 Linear Algebra and its Applications 10 Algebras and Representation Theory 9 International Journal of Theoretical Physics 9 Journal of Mathematical Sciences (New York) 9 The Journal of Fourier Analysis and Applications 9 The Ramanujan Journal 8 Advances in Applied Clifford Algebras 7 Physics Letters. A 6 Communications in Algebra 6 Israel Journal of Mathematics 6 Ukrainian Mathematical Journal 6 Reviews in Mathematical Physics 6 Representation Theory 6 International Journal of Geometric Methods in Modern Physics 5 Modern Physics Letters A 5 Journal of Approximation Theory 5 Annales Henri Poincaré 5 Journal of Noncommutative Geometry 4 Physics Letters. B 4 Annales de l’Institut Fourier 4 Duke Mathematical Journal 4 Proceedings of the American Mathematical Society 4 Acta Applicandae Mathematicae 4 Annals of Physics 4 Indagationes Mathematicae. New Series 4 Applied and Computational Harmonic Analysis 4 Selecta Mathematica. New Series 4 Journal of Nonlinear Mathematical Physics 4 Complex Analysis and Operator Theory 4 Journal of Function Spaces 3 Physica A 3 Compositio Mathematica 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 3 Advances in Applied Mathematics 3 International Journal of Mathematics 3 Expositiones Mathematicae 3 Journal of Inequalities and Applications 3 Annals of Mathematics. Second Series 3 Journal of Algebra and its Applications 3 Journal of Physics A: Mathematical and Theoretical 3 Journal of \(K\)-Theory 3 AIMS Mathematics 2 International Journal of Modern Physics A 2 Mathematical Notes 2 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section A. Physique Théorique 2 Applied Mathematics and Computation 2 International Journal of Mathematics and Mathematical Sciences 2 Integral Equations and Operator Theory 2 Journal of Combinatorial Theory. Series A 2 Journal of Multivariate Analysis 2 Journal of Number Theory 2 Mathematische Annalen 2 Mathematische Nachrichten 2 Mathematische Zeitschrift 2 Monatshefte für Mathematik 2 Statistics & Probability Letters 2 Chinese Annals of Mathematics. Series B 2 Probability Theory and Related Fields 2 Applied Mathematics Letters 2 Forum Mathematicum 2 The Journal of Geometric Analysis 2 Godishnik na Sofiĭskiya Universitet “Sv. Kliment Okhridski”. Fakultet po Matematika i Informatika 2 Computational Mathematics and Mathematical Physics 2 Journal of Algebraic Combinatorics 2 Integral Transforms and Special Functions 2 Boletín de la Sociedad Matemática Mexicana. Third Series 2 Documenta Mathematica 2 Iranian Journal of Science and Technology. Transaction A: Science 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Advances in Difference Equations 2 Foundations of Physics 2 Banach Journal of Mathematical Analysis 2 Advances in Mathematical Physics 2 Science China. Mathematics 2 Forum of Mathematics, Sigma 1 Applicable Analysis 1 Computers & Mathematics with Applications 1 Computer Physics Communications 1 Discrete Mathematics 1 Inverse Problems 1 Journal d’Analyse Mathématique 1 Journal of Statistical Physics 1 Linear and Multilinear Algebra 1 Mathematical Methods in the Applied Sciences ...and 103 more Serials all top 5 Cited in 56 Fields 326 Quantum theory (81-XX) 279 Nonassociative rings and algebras (17-XX) 181 Special functions (33-XX) 137 Topological groups, Lie groups (22-XX) 131 Associative rings and algebras (16-XX) 86 Functional analysis (46-XX) 83 Group theory and generalizations (20-XX) 70 Global analysis, analysis on manifolds (58-XX) 43 Combinatorics (05-XX) 38 Harmonic analysis on Euclidean spaces (42-XX) 38 Statistical mechanics, structure of matter (82-XX) 37 Abstract harmonic analysis (43-XX) 35 Operator theory (47-XX) 31 Probability theory and stochastic processes (60-XX) 29 Relativity and gravitational theory (83-XX) 28 Partial differential equations (35-XX) 27 Algebraic geometry (14-XX) 27 Linear and multilinear algebra; matrix theory (15-XX) 26 Differential geometry (53-XX) 23 Integral transforms, operational calculus (44-XX) 20 Category theory; homological algebra (18-XX) 18 Numerical analysis (65-XX) 17 Difference and functional equations (39-XX) 17 Approximations and expansions (41-XX) 17 Manifolds and cell complexes (57-XX) 16 Number theory (11-XX) 16 Functions of a complex variable (30-XX) 14 Dynamical systems and ergodic theory (37-XX) 11 \(K\)-theory (19-XX) 11 Statistics (62-XX) 10 Ordinary differential equations (34-XX) 9 Several complex variables and analytic spaces (32-XX) 8 Real functions (26-XX) 6 Geometry (51-XX) 6 Convex and discrete geometry (52-XX) 6 Mechanics of particles and systems (70-XX) 5 Algebraic topology (55-XX) 5 Computer science (68-XX) 5 Biology and other natural sciences (92-XX) 4 Astronomy and astrophysics (85-XX) 4 Operations research, mathematical programming (90-XX) 4 Information and communication theory, circuits (94-XX) 3 Mathematical logic and foundations (03-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Commutative algebra (13-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Field theory and polynomials (12-XX) 1 Measure and integration (28-XX) 1 Integral equations (45-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Geophysics (86-XX) 1 Systems theory; control (93-XX) Citations by Year