Admissible subsets and Littelmann paths in affine Kazhdan-Lusztig theoryReportar como inadecuado




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1 Algebre LMPT - Laboratoire de Mathématiques et Physique Théorique

Abstract : The center of an extended affine Hecke algebra is known to be isomorphic to the ring of symmetric functions associated to the underlying finite Weyl group W0. The set of Weyl characters s λ forms a basis of the center and this character acts as translation on the Kazhdan-Lusztig basis element Cw 0 where w0 is the longest element of W0, that is we have s λ Cw 0 = Cp λ w 0. As a consequence, we see that the coefficients that appears when decomposing sτ s λ Cw 0 = sτ Cp λ w 0 in the Kazhdan-Lusztig basis are tensor multiplicities of the Lie algebra with Weyl group W0. The aim of this paper is to explain how admissible subsets and Littelmann paths, which are models to compute such multiplicities, naturally appear when working out the decomposition of sτ Cp λ w 0 in the Kazhdan-Lusztig basis.

Keywords : Kazhdan-Lusztig basis affine Weyl groups admissible subsets Littelmann paths





Autor: Jeremie Guilhot -

Fuente: https://hal.archives-ouvertes.fr/



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