Littlewood–Richardson Coefficients and Kazhdan–Lusztig Polynomials

Leclerc, Bernard; Thibon, Jean-Yves

doi:10.2969/aspm/02810155

VOL. 28 | 2000 Littlewood–Richardson Coefficients and Kazhdan–Lusztig Polynomials

Chapter Author(s) Bernard Leclerc, Jean-Yves Thibon

Editor(s) Kazuhiko Koike, Masaki Kashiwara, Soichi Okada, Itaru Terada, Hiro-Fumi Yamada

Adv. Stud. Pure Math., 2000: 155-220 (2000) DOI: 10.2969/aspm/02810155

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 [21] in terms of ribbon tableaux.