Fakhri, Hossein; Nouraddini, Mojtaba From the Wigner-Eckart theorem to the Hilbert-Schmidt scalar product for an adjoint representation of the quantum algebra \(U_{p,q}(su_2)\). (English) Zbl 1359.17026 Int. J. Geom. Methods Mod. Phys. 13, No. 10, Article ID 1650127, 12 p. (2016). Reviewer: J. N. Alonso Alvarez (Vigo) MSC: 17B37 81R50 PDFBibTeX XMLCite \textit{H. Fakhri} and \textit{M. Nouraddini}, Int. J. Geom. Methods Mod. Phys. 13, No. 10, Article ID 1650127, 12 p. (2016; Zbl 1359.17026) Full Text: DOI
Bouzas, Antonio O. The Wigner-Eckart theorem for reducible symmetric Cartesian tensor operators. (English) Zbl 1351.81057 Rep. Math. Phys. 78, No. 1, 69-105 (2016). MSC: 81R05 81Q10 33C55 PDFBibTeX XMLCite \textit{A. O. Bouzas}, Rep. Math. Phys. 78, No. 1, 69--105 (2016; Zbl 1351.81057) Full Text: DOI arXiv
Fakhri, H.; Nouraddini, M. Right \(SU_q(2)\)- and left \(SU_{q^{-1}}(2)\)-invariances of the \(q\)-Hilbert-Schmidt scalar products for an adjoint representation of the quantum algebra \(\breve{U}_q(su_2)\). (English) Zbl 1364.57027 J. Geom. Phys. 110, 90-100 (2016). Reviewer: Vida Milani (North Logan) MSC: 57T05 16T05 17B37 81R50 PDFBibTeX XMLCite \textit{H. Fakhri} and \textit{M. Nouraddini}, J. Geom. Phys. 110, 90--100 (2016; Zbl 1364.57027) Full Text: DOI
Damnjanović, Milan; Milošević, Ivanka Full symmetry implementation in condensed matter and molecular physics-modified group projector technique. (English) Zbl 1357.81107 Phys. Rep. 581, 1-43 (2015). MSC: 81R05 20C35 PDFBibTeX XMLCite \textit{M. Damnjanović} and \textit{I. Milošević}, Phys. Rep. 581, 1--43 (2015; Zbl 1357.81107) Full Text: DOI
Fakhri, H.; Nouraddini, M. Scalar product for the tensor operators of the quantum algebra \(\breve{U}_{q}(\mathrm{su}_{2})\) by the Wigner-Eckart theorem. (English) Zbl 1329.81239 Int. J. Geom. Methods Mod. Phys. 12, No. 10, Article ID 1550107, 6 p. (2015). MSC: 81R50 17B37 22E70 16T05 46L60 47B10 PDFBibTeX XMLCite \textit{H. Fakhri} and \textit{M. Nouraddini}, Int. J. Geom. Methods Mod. Phys. 12, No. 10, Article ID 1550107, 6 p. (2015; Zbl 1329.81239) Full Text: DOI
Sellaroli, Giuseppe Wigner-Eckart theorem for the non-compact algebra \(\mathfrak{sl}(2,\mathbb{R})\). (English) Zbl 1315.81050 J. Math. Phys. 56, No. 4, 041701, 19 p. (2015). Reviewer: Dmitri Artamonov (Moskva) MSC: 81R05 17B81 22E43 22E70 PDFBibTeX XMLCite \textit{G. Sellaroli}, J. Math. Phys. 56, No. 4, 041701, 19 p. (2015; Zbl 1315.81050) Full Text: DOI arXiv
Cvitanović, Predrag Group theory. Birdtracks, Lie’s, and exceptional groups. (English) Zbl 1152.22001 Princeton, NJ: Princeton University Press (ISBN 978-0-691-11836-9/hbk). xii, 273 p. (2008). Reviewer: Eugene Kryachko (Liège) MSC: 22-02 17-02 17Bxx 20-01 20-02 20B30 20B35 22Exx 81Rxx 81Q30 81Vxx PDFBibTeX XMLCite \textit{P. Cvitanović}, Group theory. Birdtracks, Lie's, and exceptional groups. Princeton, NJ: Princeton University Press (2008; Zbl 1152.22001)
Krutov, A. F.; Troitsky, V. E. Construction of form factors of composite systems by a generalized Wigner-Eckart theorem for the Poincaré group. (English) Zbl 1178.81290 Theor. Math. Phys. 143, No. 2, 704-719 (2005); translation from Teor. Mat. Fiz. 143, No. 2, 258-277 (2005). MSC: 81V15 81R05 PDFBibTeX XMLCite \textit{A. F. Krutov} and \textit{V. E. Troitsky}, Theor. Math. Phys. 143, No. 2, 704--719 (2005; Zbl 1178.81290); translation from Teor. Mat. Fiz. 143, No. 2, 258--277 (2005) Full Text: DOI arXiv
Mozrzymas, Marek Wigner-Eckart theorem for tensor operators of Hopf algebras. (English) Zbl 1075.16018 Int. J. Geom. Methods Mod. Phys. 2, No. 3, 393-408 (2005). MSC: 16W30 81R50 17B37 PDFBibTeX XMLCite \textit{M. Mozrzymas}, Int. J. Geom. Methods Mod. Phys. 2, No. 3, 393--408 (2005; Zbl 1075.16018) Full Text: DOI arXiv
Iorgov, N. Z. On tensor products of representations of the non-standard \(q\)-deformed algebra \(U_q'(\text{so}_n)\). (English) Zbl 0997.81042 J. Phys. A, Math. Gen. 34, No. 14, 3095-3108 (2001). MSC: 81R50 PDFBibTeX XMLCite \textit{N. Z. Iorgov}, J. Phys. A, Math. Gen. 34, No. 14, 3095--3108 (2001; Zbl 0997.81042) Full Text: DOI
Hecht, Karl T. Quantum mechanics. (English) Zbl 0964.81001 Graduate Texts in Contemporary Physics. New York, NY: Springer. xix, 760 p. (2000). Reviewer: V.Balan (Bucureşti) MSC: 81-01 81Q05 81R05 81U05 81V05 PDFBibTeX XMLCite \textit{K. T. Hecht}, Quantum mechanics. New York, NY: Springer (2000; Zbl 0964.81001)
Mukunda, N. Group theoretical aspects of the geometric phase in quantum mechanics. (English) Zbl 0983.81026 Corney, S. P. (ed.) et al., Group 22: Proceedings of the XXII international colloquium on group theoretical methods in physics held in Hobart, Australia, July 13-17, 1998. Cambridge, MA: International Press. 86-96 (1999). MSC: 81Q70 81R05 PDFBibTeX XMLCite \textit{N. Mukunda}, in: Group 22: Proceedings of the XXII international colloquium on group theoretical methods in physics held in Hobart, Australia, July 13--17, 1998. Cambridge, MA: International Press. 86--96 (1999; Zbl 0983.81026)
Aizawa, N. Tensor operators for \(\mathcal U_h(\text{sl}(2))\). (English) Zbl 0988.17010 J. Phys. A, Math. Gen. 31, No. 24, 5467-5475 (1998). MSC: 17B37 81R50 PDFBibTeX XMLCite \textit{N. Aizawa}, J. Phys. A, Math. Gen. 31, No. 24, 5467--5475 (1998; Zbl 0988.17010) Full Text: DOI arXiv
Cornwell, J. F. Irreducible tensor operators in the regular coaction formalisms of compact quantum group algebras. (English) Zbl 0947.17006 J. Math. Phys. 37, No. 9, 4590-4634 (1996). Reviewer: J.Repka (Toronto) MSC: 17B37 81R50 46L89 22E46 PDFBibTeX XMLCite \textit{J. F. Cornwell}, J. Math. Phys. 37, No. 9, 4590--4634 (1996; Zbl 0947.17006) Full Text: DOI arXiv
Bytsko, A. G.; Faddeev, L. D. \((T^*\mathcal{B})_ q\), \(q\)-analog of model space and the Clebsch-Gordan coefficients generating matrices. (English) Zbl 0873.17018 J. Math. Phys. 37, No. 12, 6324-6348 (1996). Reviewer: A.A.Bogush (Minsk) MSC: 17B37 81R50 22E60 PDFBibTeX XMLCite \textit{A. G. Bytsko} and \textit{L. D. Faddeev}, J. Math. Phys. 37, No. 12, 6324--6348 (1996; Zbl 0873.17018) Full Text: DOI arXiv
Cornwell, J. F. Abstract carrier space formalism for the irreducible tensor operators of compact quantum group algebras. (English) Zbl 0947.17007 J. Math. Phys. 37, No. 6, 2934-2954 (1996). Reviewer: J.Repka (Toronto) MSC: 17B37 81R50 46L89 22E46 PDFBibTeX XMLCite \textit{J. F. Cornwell}, J. Math. Phys. 37, No. 6, 2934--2954 (1996; Zbl 0947.17007) Full Text: DOI arXiv
Klein, D. J. Algebraic techniques for group theory. (English) Zbl 0871.20009 Bonchev, Danail (ed.) et al., Chemical group theory: techniques and applications. Reading: Gordon and Breach Publishers. Math. Chem. Ser. 4, 1-35 (1995). Reviewer: E.Weimar-Woods (Berlin) MSC: 20C35 PDFBibTeX XMLCite \textit{D. J. Klein}, Math. Chem. Ser. 4, 1--35 (1995; Zbl 0871.20009)
Ruegg, H.; Tolstoy, V. N. Representation theory of quantized Poincaré algebra. Tensor operators and their applications to one-particle systems. (English) Zbl 0826.16038 Lett. Math. Phys. 32, No. 2, 85-101 (1994). MSC: 16W30 17B37 81R50 17B81 PDFBibTeX XMLCite \textit{H. Ruegg} and \textit{V. N. Tolstoy}, Lett. Math. Phys. 32, No. 2, 85--101 (1994; Zbl 0826.16038) Full Text: DOI arXiv
Nomura, Masao Covariant quantum algebras. (English) Zbl 0853.17015 Gruber, Bruno (ed.), Symmetries in science VI: From the rotation group to quantum algebras. Proceedings of a symposium held in Bregenz, Austria, August 2-7, 1992. New York, NY: Plenum Press. 537-551 (1993). Reviewer: Ma Zhong-Qi (Beijing) MSC: 17B37 81R50 81R30 33D80 PDFBibTeX XMLCite \textit{M. Nomura}, in: Symmetries in science VI: from the rotation group to quantum algebras. Proceedings of a symposium held in Bregenz, Austria, August 2-7, 1992. New York, NY: Plenum Press. 537--551 (1993; Zbl 0853.17015)
Aizawa, N. Tensor operators and Clebsch-Gordan coefficients of the quantum algebra \(su_ q(1,1)\). (English) Zbl 0785.17008 J. Math. Phys. 34, No. 5, 1937-1963 (1993). Reviewer: A.Klimyk (Kiev) MSC: 17B37 81R50 PDFBibTeX XMLCite \textit{N. Aizawa}, J. Math. Phys. 34, No. 5, 1937--1963 (1993; Zbl 0785.17008) Full Text: DOI
Pan, Feng; Chen, Jinquan Symmetric irreducible representations of \(SU(3)_ q\) in the \(SU(2)_ q \times{}U(1)\) basis and some extensions to \(SU(N)_ q \supset{}SU(N- 1)_ q \times{}U(1)\). (English) Zbl 0761.17015 J. Phys. A, Math. Gen. 25, No. 14, 4017-4024 (1992). MSC: 17B37 81R50 PDFBibTeX XMLCite \textit{F. Pan} and \textit{J. Chen}, J. Phys. A, Math. Gen. 25, No. 14, 4017--4024 (1992; Zbl 0761.17015) Full Text: DOI
Klimyk, A. U. Wigner-Eckart theorem for the quantum group \(U_ q(n)\). (English) Zbl 0761.17013 J. Phys. A, Math. Gen. 25, No. 10, 2919-2927 (1992). MSC: 17B37 81R50 PDFBibTeX XMLCite \textit{A. U. Klimyk}, J. Phys. A, Math. Gen. 25, No. 10, 2919--2927 (1992; Zbl 0761.17013) Full Text: DOI
Biedenharn, L. C.; Lohe, M. A. Induced representations and tensor operators for quantum groups. (English) Zbl 0757.17010 Quantum groups, Proc. Workshops, Euler Int. Math. Inst. Leningrad/USSR 1990, Lect. Notes Math. 1510, 197-209 (1992). Reviewer: A.Klimyk (Kiev) MSC: 17B37 81R50 PDFBibTeX XMLCite \textit{L. C. Biedenharn} and \textit{M. A. Lohe}, Lect. Notes Math. 1510, 197--209 (1992; Zbl 0757.17010)
Brągiel, Kazimierz On the Wigner-Eckart theorem for tensor operators connected with compact matrix quantum groups. (English) Zbl 0726.22018 Lett. Math. Phys. 21, No. 3, 181-191 (1991). MSC: 22E70 81R50 17B37 22D99 PDFBibTeX XMLCite \textit{K. Brągiel}, Lett. Math. Phys. 21, No. 3, 181--191 (1991; Zbl 0726.22018) Full Text: DOI
Hoffmann, P. Generalization of Steven’s operator-equivalent method. (English) Zbl 0741.33013 J. Phys. A, Math. Gen. 24, No. 1, 35-44 (1991). Reviewer: E.Elizalde (Barcelona) MSC: 33C80 22E70 PDFBibTeX XMLCite \textit{P. Hoffmann}, J. Phys. A, Math. Gen. 24, No. 1, 35--44 (1991; Zbl 0741.33013) Full Text: DOI
Stedman, Geoffrey E. Diagram techniques in group theory. (English) Zbl 0699.20013 Cambridge etc.: Cambridge University Press. xii, 308 p. £55.00; $ 95.00 (1990). Reviewer: N.Backhouse MSC: 20C35 81S40 20-01 22E70 81R10 81Q30 81T08 PDFBibTeX XMLCite \textit{G. E. Stedman}, Diagram techniques in group theory. Cambridge etc.: Cambridge University Press (1990; Zbl 0699.20013)
Sun, Hongzhou; Zhang, Mei; Han, Qizhi; Long, Guilu A new recursion relation of CFP for the system of identical bosons. (English) Zbl 0708.22014 J. Phys. A, Math. Gen. 22, No. 22, 4769-4775 (1989). MSC: 22E70 22E46 PDFBibTeX XMLCite \textit{H. Sun} et al., J. Phys. A, Math. Gen. 22, No. 22, 4769--4775 (1989; Zbl 0708.22014) Full Text: DOI
Vanthournout, J.; Van der Jeugt, Joris; De Meyer, H.; Vanden Berghe, G. On the spectrum of a third-order \(\mathrm{SO}(3)\) scalar in the enveloping algebra of \(\mathrm{SO}(6)\). (English) Zbl 0649.22013 J. Math. Phys. 29, No. 4, 802-805 (1988). Reviewer: Gert Roepstorff (Aachen) MSC: 22E70 81V35 81T40 17B81 PDFBibTeX XMLCite \textit{J. Vanthournout} et al., J. Math. Phys. 29, No. 4, 802--805 (1988; Zbl 0649.22013) Full Text: DOI
Angelova, M. N.; Aroyo, M. I.; Kotzev, J. N. On the Wigner-Eckart theorem and coupled tensor operators for corepresentations of Shubnikov groups. (English) Zbl 0672.20023 Group theoretical methods in physics, Proc. 3rd Semin., Yurmala/USSR 1985, Vol. 2, 433-439 (1986). MSC: 20H15 20G45 PDFBibTeX XML
Rosensteel, G. Tensor operators for noncompact Lie groups. (English) Zbl 0664.22033 Group theoretical methods in physics, Proc. 14th Int. Colloq., Seoul/Korea 1985, 326-329 (1986). MSC: 22E70 22E47 81V35 PDFBibTeX XML
Barut, Asim O.; Raczka, Ryszard Theory of group representations and applications. 2nd rev. ed. (English) Zbl 0644.22011 Singapore: World Scientific. XIX, 717 p. (1986). MSC: 22E70 22-02 81R10 PDFBibTeX XML
Angelova, M. N.; Aroyo, M. I.; Kotzev, J. N. On the factorisation of matrix elements for systems with anti-unitary symmetry. (English) Zbl 0611.22016 J. Phys. A 19, 1279-1289 (1986). MSC: 22E70 PDFBibTeX XMLCite \textit{M. N. Angelova} et al., J. Phys. A, Math. Gen. 19, 1279--1289 (1986; Zbl 0611.22016) Full Text: DOI
Guichardet, A. Sur les règles de sélection en spectroscopie moléculaire de vibration et de rotation. (On selection rules in vibrational and rotational molecular spectroscopy). (French) Zbl 0606.58053 Ann. Inst. Henri Poincaré, Phys. Théor. 44, 91-101 (1986). MSC: 58J90 58J70 81V55 PDFBibTeX XMLCite \textit{A. Guichardet}, Ann. Inst. Henri Poincaré, Phys. Théor. 44, 91--101 (1986; Zbl 0606.58053) Full Text: Numdam EuDML
Cornwell, J. F. Group theory in physics. Vols. I, II. (English) Zbl 0557.20001 Techniques of Physics, 7. London-Orlando etc.: Academic Press (Harcourt Brace Jovanovich, Publishers). Vol. I: xvi, 371, xxviii p. $ 75.00; £49.50 (1984); Vol. II: xvi, pp. 375-933, xxviii p. $ 100.00; £70.00 (1984). Reviewer: Nigel B. Backhouse MSC: 20-01 17-01 22-01 81-01 20C35 20G45 20H15 17B10 17B45 22E70 81Rxx PDFBibTeX XML
Klimyk, A. U. Wigner-Eckart theorem and infinitesimal operators of group representations. (English) Zbl 0578.22025 J. Phys. A 16, 3693-3702 (1983). Reviewer: L. C. Biedenharn (Durham, NC) MSC: 22E70 81R10 PDFBibTeX XMLCite \textit{A. U. Klimyk}, J. Phys. A, Math. Gen. 16, 3693--3702 (1983; Zbl 0578.22025) Full Text: DOI
Gould, M. D. Wigner coefficients for a semisimple Lie group and the matrix elements of the \(O(n)\) generators. (English) Zbl 0504.22017 J. Math. Phys. 22, 2376-2388 (1981). MSC: 22E70 22D10 81R10 22C05 22E46 PDFBibTeX XMLCite \textit{M. D. Gould}, J. Math. Phys. 22, 2376--2388 (1981; Zbl 0504.22017) Full Text: DOI
Biedenharn, L. C.; Louck, J. D. [Carruthers, P. A.] Angular momentum in quantum physics. Theory and application. With a foreword by Peter A. Carruthers. (English) Zbl 0474.00023 Encyclopedia of Mathematics and Its Applications, Vol. 8. Section: Mathematics of Physics. Reading, Massachusetts: etc.: Addison-Wesley Publishing Company, Advanced Book Program. XXXII, 716 p. (1981). MSC: 00A79 81-02 81V45 22E70 22-02 00-02 33C55 81T60 81V35 81V55 PDFBibTeX XML
Newmarch, J. D.; Golding, R. M. The Racah algebra for groups with time reversal symmetry. (English) Zbl 0468.22017 J. Math. Phys. 22, 233-244 (1981). MSC: 22E70 22C05 PDFBibTeX XMLCite \textit{J. D. Newmarch} and \textit{R. M. Golding}, J. Math. Phys. 22, 233--244 (1981; Zbl 0468.22017) Full Text: DOI Link
Barut, Asim O.; Raczka, Ryszard Theory of group representations and applications. 2nd rev. ed. (English) Zbl 0471.22021 Warszawa: PWN-Polish Scientific Publishers. XIX, 717 p. DM 98.50; $ 56.00 (1980). MSC: 22E70 22-02 81R10 PDFBibTeX XML Backlinks: MO
Agrawala, Vishnu K. Wigner-Eckart theorem for an arbitrary group or Lie algebra. (English) Zbl 0452.22013 J. Math. Phys. 21, 1562-1565 (1980). MSC: 22E45 22E70 81T60 22E20 PDFBibTeX XMLCite \textit{V. K. Agrawala}, J. Math. Phys. 21, 1562--1565 (1980; Zbl 0452.22013) Full Text: DOI
Weinert, Ulrich Spherical tensor representation. (English) Zbl 0447.15018 Arch. Ration. Mech. Anal. 74, 165-196 (1980). MSC: 15A72 53A45 33C55 20C35 81R10 PDFBibTeX XMLCite \textit{U. Weinert}, Arch. Ration. Mech. Anal. 74, 165--196 (1980; Zbl 0447.15018) Full Text: DOI
Prasad, L. S. R. K.; Bharathi, K. \(6j\) symbols and \(3jm\) factors for the group chain \(D_{4d}\supset D_4\subset C_4\). (English) Zbl 0432.20009 J. Phys. A 13, 781-788 (1980). MSC: 20C35 22E70 81R10 PDFBibTeX XMLCite \textit{L. S. R. K. Prasad} and \textit{K. Bharathi}, J. Phys. A, Math. Gen. 13, 781--788 (1980; Zbl 0432.20009) Full Text: DOI
Agrawala, Vishnu K. Wigner-Eckart theorem for graded generalized Lie algebras. (English) Zbl 0417.17004 Hadronic J. 2, 830-839 (1979). MSC: 17A70 17B70 17B15 81V25 PDFBibTeX XMLCite \textit{V. K. Agrawala}, Hadronic J. 2, 830--839 (1979; Zbl 0417.17004)