Article contents
Lusztig’s a-Function in Type Bn in the Asymptotic Case
Published online by Cambridge University Press: 11 January 2016
Abstract
In this paper, we study Lusztig’s a-function for a Coxeter group with unequal parameters. We determine that function explicitly in the “asymptotic case” in type Bn, where the left cells have been determined in terms of a generalized Robinson-Schensted correspondence by Bonnafé and the second author. As a consequence, we can show that all of Lusztig’s conjectural properties (P1)–(P15) hold in this case, except possibly (P9), (P10) and (P15). Our methods rely on the “leading matrix coefficients” introduced by the first author. We also interprete the ideal structure defined by the two-sided cells in the associated Iwahori-Hecke algebra Hn in terms of the Dipper-James-Murphy basis of Hn.
- Type
- Research Article
- Information
- Nagoya Mathematical Journal , Volume 182: Special Issue Celebrating the 60th Birthday of George Lusztig , June 2006 , pp. 199 - 240
- Copyright
- Copyright © Editorial Board of Nagoya Mathematical Journal 2006
References
- 11
- Cited by