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The Path Model for Representations of Symmetrizable Kac-Moody Algebras

In: Proceedings of the International Congress of Mathematicians

Author

Listed:
  • Peter Littelmann

    (Universität Basel, Mathematisches Institut
    Université Louis Pasteus, IRMA)

Abstract

In the theory of finite-dimensional representations of complex reductive algebraic groups, the group GL n (ℂ) is singled out by the fact that besides the usual language of weight lattices, roots, and characters, there exists an additional important combinatorial tool: the Young tableaux. For example, the sum over the weights of all tableaux of a fixed shape is the character of the corresponding representation, and the Littlewood-Richardson rule describes the decomposition of tensor products of GL n (ℂ)-modules purely in terms of the combinatoric of these Young tableaux. The advantage of this type of formula is (for example compared to Steinberg’s formula to decompose tensor products) that there is no cancellation of terms. This makes it much easier (and sometimes even possible) to prove for example that certain representations occur in a given tensor product.

Suggested Citation

  • Peter Littelmann, 1995. "The Path Model for Representations of Symmetrizable Kac-Moody Algebras," Springer Books, in: S. D. Chatterji (ed.), Proceedings of the International Congress of Mathematicians, pages 298-308, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-9078-6_23
    DOI: 10.1007/978-3-0348-9078-6_23
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