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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Zones of uniform decomposition in tensor products


Author: Alex Jay Feingold
Journal: Proc. Amer. Math. Soc. 70 (1978), 109-113
MSC: Primary 17B10
DOI: https://doi.org/10.1090/S0002-9939-1978-0472943-2
MathSciNet review: 0472943
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Abstract: Let $ {V_\lambda }$ be a finite dimensional irreducible module for a complex semisimple Lie algebra. It is shown that the decomposition of tensor products $ {V_\lambda } \otimes {V_\tau }$ for all dominant integral weights $ \tau $ may be derived from those for a finite set of such $ \tau $. An explicit choice of such a finite set (depending on $ \lambda $) is given.


References [Enhancements On Off] (What's this?)

  • [1] R. Brauer, Sur la multiplication des caractéristiques des groupes continus et semi-simples, C. R. Acad. Sci. Paris Sér A-B 204 (1937), 1784-1786.
  • [2] J. E. Humphreys, Introduction to Lie algebras and representation theory, Graduate Texts in Math., no. 9, Springer-Verlag, New York, 1972. MR 0323842 (48:2197)
  • [3] A. U. Klimyk, Decomposition of a tensor product of irreducible representations of a semisimple Lie algebra into a direct sum of irreducible representations, Ukrain. Mat. Ž. 18 (1966), 19-27; English transl., Amer. Math. Soc. Transl. (2) 76 (1968), 63-73. MR 0206169 (34:5991)
  • [4] B. Kostant, A formula for the multiplicity of a weight, Trans. Amer. Math. Soc. 93 (1959), 53-73. MR 0109192 (22:80)

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DOI: https://doi.org/10.1090/S0002-9939-1978-0472943-2
Article copyright: © Copyright 1978 American Mathematical Society

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