Automorphisms of Coxeter groups and Lusztig's conjectures for Hecke algebras with unequal parameters

Details Automorphisms of Coxeter groups and Lusztig's conjectures for Hecke algebras with unequal parameters Automorphisms of Coxeter groups and Lusztig's conjectures for Hecke algebras with unequal parameters

2008-05-28

arxiv.org/abs/0805.4269v3

Mathematics

Representation Theory

11 pages, few misprints corrected

Scientific paper

Let $(W,S)$ be a Coxeter system, let $G$ be a finite solvable group of automorphisms of $(W,S)$ and let $\varphi$ be a weight function which is invariant under $G$. Let $\varphi_G$ denote the weight function on $W^G$ obtained by restriction from $\varphi$. The aim of this paper is to compare the ${\mathbf{a}}$-function, the set of Duflo involutions and the Kazhdan-Lusztig cells associated to $(W,\varphi)$ and to $(W^G,\varphi_G)$, provided that Lusztig's Conjectures hold.

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