Parabolic Kazhdan-Lusztig polynomials for quasi-minuscule quotients

摘要

We study the parabolic Kazhdan-Lusztig polynomials for the quasi-minuscule quotients of Weyl groups. We give explicit closed combinatorial formulas for the parabolic Kazhdan-Lusztig polynomials of type q. Our study implies that these are always either zero or a monic power of q, and that they are not combinatorial invariants. We conjecture a combinatorial interpretation for the parabolic Kazhdan-Lusztig polynomials of type -1. (C) 2016 Elsevier Inc. All rights reserved.