W-graph ideals and duality

JOURNAL OF ALGEBRA

卷:453

Article

Yin, Yunchuan¹ 

[1] Shanghai Univ Finance & Econ, Dept Math, 777 Guoding Rd, Shanghai 200433, Peoples R China

关键词: Coxeter group;    Hecke algebra;    W-graph;    Kazhdan-Lusztig basis;    Kazhdan-Lusztig polynomial;   

DOI  :  10.1016/j.jalgebra.2015.12.021

来源: Elsevier

【 摘 要 】

This paper is the continuation of the work in [14]. In that paper we generalized the definition of W-graph ideal in the weighted Coxeter groups, and showed how to construct a W-graph from a given W-graph ideal in the case of unequal parameters. In this paper we study the duality and the full W-graph for a given W-graph ideal. We show that there are two modules associated with a given W-graph ideal, they are connected by a duality map. The full W-graph includes all the W-graph data determined by the dual and contragredient representations. Our construction closely parallels that of Kazhdan and Lusztig [6,10,11], which can be regarded as the special case J = empty set. It also generalizes the work of Couillens [2], Deodhar [3,4], and Douglass [5], corresponding to the parabolic case. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free