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Lusztig’s a-Function in Type Bn in the Asymptotic Case

Published online by Cambridge University Press:  11 January 2016

Meinolf Geck  and
Lacrimioara Iancu
Meinolf Geck*
Affiliation:
Institut Camille Jordan, Université Lyon 1, 21 av Claude Bernard, 69622 Villeurbanne cedex, France
Lacrimioara Iancu*
Affiliation:
IGAT, EPFL, Bâtiment de chimie, 1015 Lausanne, Switzerland
*
Department of Mathematical Sciences, King’s College, Aberdeen University, Aberdeen AB24 3UE, Scotland, U.K., m.geck@maths.abdn.ac.uk
Department of Mathematical Sciences, King’s College, Aberdeen University, Aberdeen AB24 3UE, Scotland, U.K., l.iancu@maths.abdn.ac.uk
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Abstract

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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.

Keywords

20C0820G40
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

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