Combinatorial formulas for Kazhdan-Lusztig polynomials with respect to W-graph ideals

Qi Wang

Published 2017-10-12Version 1

In [12] Yin generalized the definition of W-graph ideal $E_J$ in the weighted Coxeter groups and introduced the weighted Kazhdan-Lusztig polynomials $ \left \{ P_{x,y} \right \}_{x,y\in E_J}$, where J is a subset of S. In this paper, we study the combinatorial formulas for those polynomials, which extend the results of Deodhar [11] and Tagawa [6].