Littlewood-Richardson coefficients and Kazhdan-Lusztig polynomials

Abstract

We show that the Littlewood-Richardson coefficients are values at 1 of certain parabolic Kazhdan-Lusztig polynomials for affine symmetric groups. These q-analogues of Littlewood-Richardson multiplicities coincide with those previously introduced in terms of ribbon tableaux.Comment: 51 pages, 10 Figures, Minor corrections and typos, and some new comments concerning Soergel's character formula for tilting module