Integral u-deformed involution modules

JOURNAL OF ALGEBRA

卷:531

Article

Hu, Jun¹  Sun, Yujiao¹ 

[1] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China

关键词: Coxeter groups;    Hecke algebras;    Twisted involutions;   

DOI  :  10.1016/j.jalgebra.2019.03.041

来源: Elsevier

【 摘 要 】

Let (W, S) be a Coxeter system and * an automorphism of W with order <= 2 and S* = S. Lusztig and Vogan ([20], [23]) have introduced a u-deformed version M-u of Kottwitz's involution module over the Iwahori-Hecke algebra H-u(W) with Hecke parameter u(2), where u is an indeterminate. Lusztig has proved that M-u is isomorphic to the left H-u(W)-submodule of H-u generated by X-empty set := Sigma(w*=w is an element of W) u(-l(w))T(w), where H-u is the vector space consisting of all formal (possibly infinite) sums Sigma(x is an element of W) c(x)T(x) (c(x) is an element of Q(u) for each x). He speculated that one can extend this by replacing u with any lambda is an element of C \ {0, 1, -1}. In this paper, we give a positive answer to his speculation for any lambda is an element of K \ {0,1, -1} and any W, where K is an arbitrary ground field. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free