ADMISSIBLE SUBSETS AND LITTELMANN PATHS IN AFFINE KAZHDAN-LUSZTIG THEORY

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 W-0. The set of Weyl characters s forms a basis of the center and Lusztig showed in [11] that these characters act as translations on the Kazhdan-Lusztig basis element where w(0) is the longest element of W-0, that is, we have As a consequence, the coefficients that appear when decomposing in the Kazhdan-Lusztig basis are tensor multiplicities of the Lie algebra with Weyl group W-0. 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 this decomposition.