Invariant theory of tensor product decompositions of U(N) and generalized Casimir operators

Notices of the American Mathematical Society

Volumn 56, Issue 8, 2009, Pages 931-940

  Klink, William H ^a   Ton That, Tuong ^a  

^a UNIVERSITY OF IOWA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 68849085777     PISSN: 00029920     EISSN: 10889477     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum, World Scientific, Singapore, 1988.
2. E. P. Wigner, On the consequences of the symmetry of the nuclear Hamiltonian on the spectroscopy of nuclei, Phys. Rev. 51 (1937), 106-119; see also the review by O. W. Greenberg, From Wigner's super-multiplet theory to quantum chromodynamics, Acta Phys. Hung. A19 (2004), 353, arXiv:hep-ph/0212174.
3. M. Gell-Mann, A schematic model of baryons and mesons, Phys. Lett. 8 (1964), 214-215.
4. F. Gursey and L. A. Radicati, Spin and unitary spin independence of strong interactions, Phys. Rev. Lett. 13 (1964), 173-175.
5. S. Weinberg, The Quantum Theory of Fields, Cambridge University Press, Cambridge, 1998.
6. N. Ja. Vilenkin and A. U. Klimyk, Representations of Lie Groups and Special Functions, Recent Advances, Kluwer Academic Publishers, 1995, Chapters 5, 6.
7. W. H. Klink and T. Ton-That, On resolving the multiplicity of arbitrary tensor products of the U(N) Groups, J. Phys. A21 (1988), 3877-3892.
8. T. Ton-That, Sur la decomposition des produits tensoriels des representations irreductibles de GL(k,C), Jour. Math. Pures Appl. 56 (1977), 251-262.
9. D. P. Zelobenko, Compact Lie Groups and Their Representations (English translation in Transl. Math. Monographs), Amer. Math. Soc., Providence, R.I., 1973.
10. W. H. Klink and T. Ton-That, Multiplicity, invariants, and tensor products of compact groups, J. Math. Phys. 37 (1996), 6468-6485.
11. T. Ton-That, Dual representations and invariant theory, Contemp. Math. 191 (1995), 205-221.
12. H. Weyl, The Classical Groups, Their Invariants and Representations, 2nd ed., Princeton University Press, Princeton, N.J., 1946.
13. W. H. Klink and T. Ton-That, n-fold tensor products of GL(N,C) and decomposition of Fock spaces, J. Func. Anal. 84 (1989), 1-18.
14. R. T. Aulwes, W. H. Klink, and T. Ton-That, Invariant theory, generalized Casimir operators, and tensor product decompositions of U(N), J. Phys. A34 (2001), 8237-8257.
15. W. H. Klink and T. Ton-That, Duality in representation theory, Ulam Quart. 1 (1992), 41-49.
16. W. H. Klink and T. Ton-That, Invariant theory of the block diagonal subgroups of GL(N,C) and generalized Casimir operators, J. Algebra 145 (1992), 187-203.
17. S. Gliske, W. Klink, and T. Ton-That, Algorithms for computing generalized U(N) Racah coefficients, Acta Appl. Math. 88 (2005), 229-249.
18. S. Gliske, W. Klink, and T. Ton-That, Algorithms for computing U(N) ClebschGordan coefficients, Acta Appl. Math. 95 (2007), 51-72.