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.

51 pages, 10 Figures, Minor corrections and typos, and some new comments concerning Soergel's character formula for tilting modules