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The crystal base and Littelmann’s refined Demazure character formula. (English) Zbl 0794.17008
Demazure’s character formula describes the weight multiplicities of the \(U({\mathfrak n}^ +)\)-module generated by an extremal vector of the irreducible highest weight \(U({\mathfrak g})\)-module, where \({\mathfrak g}\) is a symmetrizable Kac-Moody Lie algebra. In his paper [Crystal graphs and Young tableaux (preprint)], P. Littelmann gives a conjecture of a generalization of the Demazure character formula which is described by crystal bases. In this paper the author proves this conjecture for any symmetrizable case.
Reviewer: H.Yamada (Tokyo)

MSC:
17B37 Quantum groups (quantized enveloping algebras) and related deformations
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
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