On Kazhdan-Lusztig polynomials for affine Weyl groups and unequal parameters

Abstract

Let H be the generic Hecke algebra corresponding to an affine Weyl group and unequal parameters. We show the existence of a canonical basis for a certain H-module M"0. The coefficients of the basis elements are generically inverses of the Kazhdan-Lusztig polynomials. We establish a formula for Kazhdan-Lusztig polynomials in terms of certain alcove polynomials. We also express certain Kazhdan-Lusztig polynomials in terms of an analogue of Kostant's partition function and prove an analogue of Kostant's weight multiplicity formula. (orig.)Available from TIB Hannover: RR 1606(96-43) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman