## Nagoya Mathematical Journal

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

Cédric Bonnafé

#### Abstract

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 with $(W, \varphi)$ and to $(W^{G}, \varphi_{G})$, provided that Lusztig's Conjectures hold.

#### Article information

Source
Nagoya Math. J., Volume 195 (2009), 153-164.

Dates
First available in Project Euclid: 14 September 2009

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1252934376

Mathematical Reviews number (MathSciNet)
MR2552958

Zentralblatt MATH identifier
1188.20002

Subjects
Primary: 20C08: Hecke algebras and their representations
Secondary: 20C15: Ordinary representations and characters

#### Citation

Bonnafé, Cédric. Automorphisms of Coxeter groups and Lusztig's conjectures for Hecke algebras with unequal parameters. Nagoya Math. J. 195 (2009), 153--164. https://projecteuclid.org/euclid.nmj/1252934376

#### References

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• G. Lusztig, Hecke algebras with unequal parameters, CRM Monograph Series 18, American Mathematical Society, Providence, RI, 2003, 136 pp.
• J. Thévenaz, $G$-Algebras and Modular Representation Theory, Clarendon Press, Oxford, 1995.