Edit Profile (opens in new tab) Gruber, Bruno J. Co-Author Distance Author ID: gruber.bruno-j Published as: Gruber, Bruno; Gruber, B.; Gruber, Bruno J. more...less Documents Indexed: 62 Publications since 1964, including 1 Book 9 Contributions as Editor · 1 Further Contribution Co-Authors: 25 Co-Authors with 45 Joint Publications 358 Co-Co-Authors all top 5 Co-Authors 25 single-authored 7 Klimyk, Anatoliy Ul’yanovich 6 Lorente, Miguel 6 Ramek, Michael 4 Lenczewski, Romuald 4 Thomas, M. Samuel 3 Doebner, Heinz-Dietrich 3 Weber, H. J. 2 Biedenharn, Lawrence C. jun. 2 Nomura, Toshio 2 O’Raifeartaigh, Lochlainn 2 Santhanam, Thalanayar S. 1 de Wolff, Pieter Maarten 1 Delaney, R. M. 1 Feinsilver, Philip J. 1 Franz, Uwe 1 Fritzer, Harald P. 1 Han, Banghe 1 Iachello, Francesco 1 Kalnins, Ernest G. 1 Kramer, Peter 1 Loebl, Ernest M. 1 Matsen, Frederick A. IV 1 McIntosh, Harold Varner 1 Millman, Richard S. 1 Moshinsky, Marcos 1 Otsuka, Takaharu 1 Patera, Jiří 1 Quesne, Christiane 1 Saldanha, J. A. 1 Samuel, M. T. 1 Schigman, T. H. 1 Sharp, Robert T. 1 Smirnov, Yu. F. 1 Wilson, Raj 1 Winternitz, Pavel 1 Wolf, Kurt Bernardo 1 Wong, M. K. F. 1 Zaccaria, Francesco all top 5 Serials 22 Journal of Mathematical Physics 7 Acta Crystallographica. Section A 5 Proceedings of the Royal Irish Academy. Section A, Mathematical and Physical Sciences 5 Kinam 4 Journal of Physics A: Mathematical and General 3 Sitzungsberichte. Abteilung II. Österreichische Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Klasse 2 Letters in Mathematical Physics 1 Computer Physics Communications 1 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section A. Physique Théorique 1 SIAM Journal on Applied Mathematics 1 Il Nuovo Cimento, X. Series 1 Il Nuovo Cimento, X. Series, A 1 Il Nuovo Cimento, Supplemento, Series I 1 Matscience Report all top 5 Fields 33 Topological groups, Lie groups (22-XX) 25 Nonassociative rings and algebras (17-XX) 23 Quantum theory (81-XX) 13 General and overarching topics; collections (00-XX) 10 Group theory and generalizations (20-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Number theory (11-XX) 2 Functional analysis (46-XX) 2 Convex and discrete geometry (52-XX) 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Associative rings and algebras (16-XX) 1 Special functions (33-XX) 1 Partial differential equations (35-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 40 Publications have been cited 229 times in 156 Documents Cited by ▼ Year ▼ S theorem and construction of the invariants of the semisimple compact Lie algebras. Zbl 0124.17401 Gruber, B.; O’Raifeartaigh, L. 35 1964 Classification of semisimple subalgebras of simple Lie algebras. Zbl 0241.17006 Lorente, M.; Gruber, B. 33 1972 A unified description of the representations of the graded Lie algebra \(\mathrm{Gsl}(2)\). Zbl 0557.17003 Gruber, Bruno; Santhanam, T. S.; Wilson, Raj 16 1984 Group theory and its applications. Vol. III. Zbl 0351.20006 12 1975 Indecomposable representations of the Lorentz algebra in an angular momentum basis. Zbl 0535.22011 Gruber, Bruno; Lenczewski, Romuald 10 1983 Boson operator realizations of su(2) and su(1,1) and unitarization. Zbl 0663.22014 Doebner, H. D.; Gruber, Bruno; Lorente, Miguel 9 1989 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 0548.22011 Klimyk, Anatoli U.; Gruber, Bruno 9 1982 Inner and restriction multiplicity for classical groups. Zbl 0206.31802 Delaney, R. M.; Gruber, B. 9 1969 Alternative formulae for the number of sublattices. Zbl 1188.05010 Gruber, B. 9 1997 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 0427.22016 Klimyk, Anatoli U.; Gruber, Bruno 9 1979 SU\(_ 4\): Clebsch-Gordan series and multiplicity \(M^ m (m')\) of a weight \(m'\) contained in the irreducible representation \(D(m)\). Zbl 0161.23804 Gruber, B. 8 1967 Matrix elements for indecomposable representations of complex su(2). Zbl 0548.17005 Gruber, Bruno; Klimyk, Anatoli U. 7 1984 Multiplicity free and finite multiplicity indecomposable representations of the algebra su(1,1). Zbl 0425.22023 Gruber, Bruno; Klimyk, A. U. 7 1978 Indecomposable representations of the Poincaré algebra. Zbl 0596.22010 Lenczewski, Romuald; Gruber, Bruno 6 1986 On an algebraic method for the decomposition of direct products of representations of the groups A\(_ 2\)(SO(5)). Zbl 0146.04103 Gruber, B. 6 1966 Properties of linear representations with a highest weight for the semisimple Lie algebras. Zbl 0308.17002 Gruber, B.; Klimyk, A. U. 5 1975 Recurrence relations for the multiplicities in the classical groups. Zbl 0194.29203 Gruber, B. 5 1970 Symmetries in science VI: from the rotation group to quantum algebras. Proceedings of a symposium held in Bregenz, Austria, August 2-7, 1992. Zbl 0835.00011 4 1993 Symmetries in science VIII. Proceedings of a symposium, Bregenz, Austria, August 1994. Zbl 0844.00030 4 1995 The relationship between reduced cells in a general Bravais lattice. Zbl 1370.82072 Gruber, B. 4 1973 Representations of the groups GL(n,R) and SU(n) in an SO(n) basis. Zbl 0485.22021 Gruber, Bruno; Klimyk, Anatoli U. 4 1981 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 0548.22009 Klimyk, A. U.; Gruber, Bruno 3 1984 Construction of extremal vectors for Verma submodules of Verma modules. Zbl 0551.17001 Lorente, Miguel; Gruber, Bruno 3 1984 Representations of the Heisenberg-Weyl algebra and group. Zbl 0502.22007 Gruber, Bruno; Doebner, H. D.; Feinsilver, Philip J. 3 1982 On the construction of weight diagrams for SO(5), Sp(4) and G\(_2\). Zbl 0258.20049 Gruber, B.; Weber, H. J. 2 1968 Multiplicities in the classical groups. I. Zbl 0204.35404 Gruber, B. 2 1970 Uniqueness of the harmonic oscillator commutation relation. Zbl 0125.45504 Gruber, B.; O’Raifeartaigh, L. 2 1964 Generating functions and characters of irreducible representations of \(\mathrm{SU}(3)\) and \(\mathrm{SU}(2,1)\). Zbl 0162.58401 Biedenharn, L. C.; Gruber, B.; Weber, H. J. 2 1968 Relations between ’inner’ and ’outer’ multiplicities for the classical groups. Zbl 0158.45803 Gruber, Bruno 2 1968 Symmetries in science VII: spectrum-generating algebras and dynamic symmetries in physics. Proceedings of a symposium held in Nakajo, Japan, August 28-31, 1992. Zbl 0835.00019 1 1993 Symmetries in science V. Algebraic systems, their representations, realizations, and physical applications. Proceedings of the symposium held in Lochau, Germany, July 30-August 3, 1990. Zbl 0930.00031 1 1991 Symmetries in science III. Papers from the symposium held in Vorarlberg, Austria, July 25-28, 1988. Zbl 0821.00014 1 1989 Symmetries in science I. Proceedings of the Einstein centennial celebration science symposium held in Carbondale, IL, USA, Feb 23-Mar 2, 1979. Zbl 1097.00519 1 1980 Symmetries in science IX. Proceedings of the international symposium, Mehrerau in Bregenz, Austria, August 6-10, 1996. Zbl 0872.00034 1 1997 Symmetry adaptation of wavefunctions and matrix elements. Zbl 0681.17006 Gruber, Bruno; Lorente, Miguel; Nomura, Toshio; Ramek, Michael 1 1988 The semisimple subalgebras of the algebra B\(_3\) (SO(7)) and their inclusion relations. Zbl 0283.17002 Gruber, Bruno 1 1974 Recurrence relation for Kostant’s formula. Zbl 0224.20039 Gruber, B.; Weber, H. J. 1 1970 Reduced cells based on extremal principles. Zbl 1191.52014 Gruber, B. 1 1989 Clebsch-Gordan series for the classical rank-two groups and SU\(_4\). Zbl 0158.45904 Gruber, B.; Zaccaria, F. 1 1967 Indecomposable representations of the algebra su(2,1). Zbl 0449.17004 Smirnov, Yu. F.; Gruber, Bruno 1 1980 Alternative formulae for the number of sublattices. Zbl 1188.05010 Gruber, B. 9 1997 Symmetries in science IX. Proceedings of the international symposium, Mehrerau in Bregenz, Austria, August 6-10, 1996. Zbl 0872.00034 1 1997 Symmetries in science VIII. Proceedings of a symposium, Bregenz, Austria, August 1994. Zbl 0844.00030 4 1995 Symmetries in science VI: from the rotation group to quantum algebras. Proceedings of a symposium held in Bregenz, Austria, August 2-7, 1992. Zbl 0835.00011 4 1993 Symmetries in science VII: spectrum-generating algebras and dynamic symmetries in physics. Proceedings of a symposium held in Nakajo, Japan, August 28-31, 1992. Zbl 0835.00019 1 1993 Symmetries in science V. Algebraic systems, their representations, realizations, and physical applications. Proceedings of the symposium held in Lochau, Germany, July 30-August 3, 1990. Zbl 0930.00031 1 1991 Boson operator realizations of su(2) and su(1,1) and unitarization. Zbl 0663.22014 Doebner, H. D.; Gruber, Bruno; Lorente, Miguel 9 1989 Symmetries in science III. Papers from the symposium held in Vorarlberg, Austria, July 25-28, 1988. Zbl 0821.00014 1 1989 Reduced cells based on extremal principles. Zbl 1191.52014 Gruber, B. 1 1989 Symmetry adaptation of wavefunctions and matrix elements. Zbl 0681.17006 Gruber, Bruno; Lorente, Miguel; Nomura, Toshio; Ramek, Michael 1 1988 Indecomposable representations of the Poincaré algebra. Zbl 0596.22010 Lenczewski, Romuald; Gruber, Bruno 6 1986 A unified description of the representations of the graded Lie algebra \(\mathrm{Gsl}(2)\). Zbl 0557.17003 Gruber, Bruno; Santhanam, T. S.; Wilson, Raj 16 1984 Matrix elements for indecomposable representations of complex su(2). Zbl 0548.17005 Gruber, Bruno; Klimyk, Anatoli U. 7 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 0548.22009 Klimyk, A. U.; Gruber, Bruno 3 1984 Construction of extremal vectors for Verma submodules of Verma modules. Zbl 0551.17001 Lorente, Miguel; Gruber, Bruno 3 1984 Indecomposable representations of the Lorentz algebra in an angular momentum basis. Zbl 0535.22011 Gruber, Bruno; Lenczewski, Romuald 10 1983 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 0548.22011 Klimyk, Anatoli U.; Gruber, Bruno 9 1982 Representations of the Heisenberg-Weyl algebra and group. Zbl 0502.22007 Gruber, Bruno; Doebner, H. D.; Feinsilver, Philip J. 3 1982 Representations of the groups GL(n,R) and SU(n) in an SO(n) basis. Zbl 0485.22021 Gruber, Bruno; Klimyk, Anatoli U. 4 1981 Symmetries in science I. Proceedings of the Einstein centennial celebration science symposium held in Carbondale, IL, USA, Feb 23-Mar 2, 1979. Zbl 1097.00519 1 1980 Indecomposable representations of the algebra su(2,1). Zbl 0449.17004 Smirnov, Yu. F.; Gruber, Bruno 1 1980 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 0427.22016 Klimyk, Anatoli U.; Gruber, Bruno 9 1979 Multiplicity free and finite multiplicity indecomposable representations of the algebra su(1,1). Zbl 0425.22023 Gruber, Bruno; Klimyk, A. U. 7 1978 Group theory and its applications. Vol. III. Zbl 0351.20006 12 1975 Properties of linear representations with a highest weight for the semisimple Lie algebras. Zbl 0308.17002 Gruber, B.; Klimyk, A. U. 5 1975 The semisimple subalgebras of the algebra B\(_3\) (SO(7)) and their inclusion relations. Zbl 0283.17002 Gruber, Bruno 1 1974 The relationship between reduced cells in a general Bravais lattice. Zbl 1370.82072 Gruber, B. 4 1973 Classification of semisimple subalgebras of simple Lie algebras. Zbl 0241.17006 Lorente, M.; Gruber, B. 33 1972 Recurrence relations for the multiplicities in the classical groups. Zbl 0194.29203 Gruber, B. 5 1970 Multiplicities in the classical groups. I. Zbl 0204.35404 Gruber, B. 2 1970 Recurrence relation for Kostant’s formula. Zbl 0224.20039 Gruber, B.; Weber, H. J. 1 1970 Inner and restriction multiplicity for classical groups. Zbl 0206.31802 Delaney, R. M.; Gruber, B. 9 1969 On the construction of weight diagrams for SO(5), Sp(4) and G\(_2\). Zbl 0258.20049 Gruber, B.; Weber, H. J. 2 1968 Generating functions and characters of irreducible representations of \(\mathrm{SU}(3)\) and \(\mathrm{SU}(2,1)\). Zbl 0162.58401 Biedenharn, L. C.; Gruber, B.; Weber, H. J. 2 1968 Relations between ’inner’ and ’outer’ multiplicities for the classical groups. Zbl 0158.45803 Gruber, Bruno 2 1968 SU\(_ 4\): Clebsch-Gordan series and multiplicity \(M^ m (m')\) of a weight \(m'\) contained in the irreducible representation \(D(m)\). Zbl 0161.23804 Gruber, B. 8 1967 Clebsch-Gordan series for the classical rank-two groups and SU\(_4\). Zbl 0158.45904 Gruber, B.; Zaccaria, F. 1 1967 On an algebraic method for the decomposition of direct products of representations of the groups A\(_ 2\)(SO(5)). Zbl 0146.04103 Gruber, B. 6 1966 S theorem and construction of the invariants of the semisimple compact Lie algebras. Zbl 0124.17401 Gruber, B.; O’Raifeartaigh, L. 35 1964 Uniqueness of the harmonic oscillator commutation relation. Zbl 0125.45504 Gruber, B.; O’Raifeartaigh, L. 2 1964 all cited Publications top 5 cited Publications all top 5 Cited by 195 Authors 18 Gruber, Bruno J. 9 Klimyk, Anatoliy Ul’yanovich 5 de Graaf, Willem Adriaan 4 Lorente, Miguel 4 Ruan, Dong 4 Wong, M. K. F. 3 Campoamor-Stursberg, Rutwig 3 Fu, Hongchen 3 Kaveh, Ali 3 Marquette, Ian 3 Marrani, Alessio 3 Santhanam, Thalanayar S. 3 Skvortsov, Evgeny D. 2 Agrawala, Vishnu K. 2 Alshammari, Fahad Sameer 2 Andrews, Lawrence C. 2 Bacher, Roland 2 Belinfante, Johan Gijsbertus Frederik 2 Bernstein, Herbert J. 2 Douglas, Andrew 2 Englefield, M. J. 2 Feinsilver, Philip J. 2 Fernández-Núñez, José 2 Frappat, Luc 2 García Fuertes, Wilfredo 2 Isaac, Phillip S. 2 Jarvis, Peter D. 2 Lenczewski, Romuald 2 Macfarlane, Alan J. 2 Mkrtchyan, Ruben L. 2 Mountain, Arthur J. 2 Okubo, Susumu 2 Paldus, Josef 2 Palev, Tchavdar D. 2 Perelomov, Askold M. 2 Plantey, R. 2 Radhakrishnan, Damu 2 Ragoucy, Eric 2 Repka, Joe 2 Ruan, Wei 2 Sauter, Nicholas K. 2 Schott, René 2 Sharapov, Alexey A. 2 Solberg, M. Aa. 2 Sorba, Paul 2 Stróż, Kazimierz 2 Veselov, Alexander Petrovich 2 Wang, Zhituo 2 Yeh, Hsin-Yang 1 Abellanas, Lorenzo 1 Alama, Jesse 1 Alekseevskiĭ, Dmitriĭ Vladimirovich 1 Amar, V. 1 Argyres, Philip C. 1 Backhouse, Nigel B. 1 Barbier, R. 1 Bärligea, Christoph Mark 1 Bars, Itzhak 1 Bayarmagnai, Gombodorj 1 Beck, Robert E. 1 Berdjis, F. 1 Biedenharn, Lawrence C. jun. 1 Bincer, Adam M. 1 Bisht, P. S. 1 Boulanger, Nicolas 1 Bracken, Anthony J. 1 Cacciatori, Sergio Luigi 1 Cahen, Michel 1 Calixto, Manuel 1 Campoleoni, Andrea 1 Cant, A. 1 Carnevale, Angela 1 Chanyal, Bhupesh Chandra 1 Chen, Linhong 1 Chen, Yuyun 1 Chuah, Meng-Kiat 1 Concha-Sánchez, Yajaira 1 Cornwell, J. F. 1 Dall’Agata, Gianguido 1 Davighi, Joe 1 de Azcárraga, José A. 1 de Fromont, Paul 1 Delaney, R. M. 1 Díaz-Bautista, Erik 1 Dietrich, Heiko 1 Doebner, Heinz-Dietrich 1 Dolan, F. A. 1 Dozzio, U. 1 Faccin, Paolo 1 Fakhri, Hossein 1 Fradkin, Efim Samoĭlovich 1 Fritzer, Harald P. 1 Fukshansky, Lenny 1 Escudero, Juan García 1 Gavrilik, Alexandre M. 1 Gawędzki, Krzysztof 1 Gerasimenko, Pavel 1 Gould, Mark D. 1 Green, Herbert S. 1 Grosse, Harald ...and 95 more Authors all top 5 Cited in 48 Serials 70 Journal of Mathematical Physics 8 Journal of High Energy Physics 5 Journal of Physics A: Mathematical and Theoretical 4 Nuclear Physics. B 4 Physica A 4 Physics Letters. A 4 Acta Crystallographica. Section A 3 Communications in Mathematical Physics 3 Reports on Mathematical Physics 3 Journal of Algebra 3 Journal of Mathematical Chemistry 2 Acta Mechanica 2 Letters in Mathematical Physics 2 Journal of Geometry and Physics 2 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section A. Physique Théorique 2 Journal of Number Theory 2 BIT. Nordisk Tidskrift for Informationsbehandling 2 Il Nuovo Cimento, X. Series, A 1 International Journal of Modern Physics A 1 Bulletin of the Australian Mathematical Society 1 Communications in Algebra 1 Computer Physics Communications 1 International Journal of Theoretical Physics 1 Journal of Computational Physics 1 Linear and Multilinear Algebra 1 Ukrainian Mathematical Journal 1 Fortschritte der Physik 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Journal of Functional Analysis 1 Journal of the Mathematical Society of Japan 1 Journal of Pure and Applied Algebra 1 Journal of Soviet Mathematics 1 Mathematische Zeitschrift 1 Monatshefte für Mathematik 1 Numerische Mathematik 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Studies in Applied Mathematics 1 Transactions of the American Mathematical Society 1 European Journal of Combinatorics 1 Journal of Symbolic Computation 1 Annals of Physics 1 Linear Algebra and its Applications 1 Advances in Engineering Software 1 Journal de Théorie des Nombres de Bordeaux 1 Selecta Mathematica. New Series 1 Transformation Groups 1 Foundations of Computational Mathematics 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris all top 5 Cited in 31 Fields 61 Nonassociative rings and algebras (17-XX) 58 Topological groups, Lie groups (22-XX) 58 Quantum theory (81-XX) 13 Group theory and generalizations (20-XX) 8 Number theory (11-XX) 7 Differential geometry (53-XX) 6 Combinatorics (05-XX) 6 Relativity and gravitational theory (83-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Special functions (33-XX) 3 Computer science (68-XX) 3 Mechanics of deformable solids (74-XX) 2 Mathematical logic and foundations (03-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Ordinary differential equations (34-XX) 2 Abstract harmonic analysis (43-XX) 2 Convex and discrete geometry (52-XX) 2 Numerical analysis (65-XX) 2 Mechanics of particles and systems (70-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Algebraic geometry (14-XX) 1 Functions of a complex variable (30-XX) 1 Partial differential equations (35-XX) 1 Geometry (51-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Classical thermodynamics, heat transfer (80-XX) Citations by Year