Zones of uniform decomposition in tensor products
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- by Alex Jay Feingold PDF
- Proc. Amer. Math. Soc. 70 (1978), 109-113 Request permission
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
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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.
- James E. Humphreys, Introduction to Lie algebras and representation theory, Graduate Texts in Mathematics, Vol. 9, Springer-Verlag, New York-Berlin, 1972. MR 0323842
- A. U. Klimyk, Decomposition of the direct product of irreducible representations of semisimple Lie algebras into irreducible representations, Ukrain. Mat. Ž. 18 (1966), no. 5, 19–27 (Russian). MR 0206169
- Bertram Kostant, A formula for the multiplicity of a weight, Trans. Amer. Math. Soc. 93 (1959), 53–73. MR 109192, DOI 10.1090/S0002-9947-1959-0109192-6
Additional Information
- © Copyright 1978 American Mathematical Society
- 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