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Representation Theory

ISSN 1088-4165



Kazhdan-Lusztig cells and decomposition numbers

Author: Meinolf Geck
Journal: Represent. Theory 2 (1998), 264-277
MSC (1991): Primary 20C20; Secondary 20G99
Published electronically: June 15, 1998
MathSciNet review: 1628035
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Abstract: We consider a generic Iwahori–Hecke algebra $H$ associated with a finite Weyl group. Any specialization of $H$ gives rise to a corresponding decomposition matrix, and we show that the problem of computing that matrix can be interpreted in terms of Lusztig’s map from $H$ to the asymptotic algebra $J$. This interpretation allows us to prove that the decomposition matrices always have a lower uni-triangular shape; moreover, we determine these matrices explicitly in the so-called defect $1$ case.

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Meinolf Geck
Affiliation: UFR de Mathématiques and UMR 7586 du CNRS, Université Paris 7, 2 Place Jussieu, 75251 Paris, France
MR Author ID: 272405

Received by editor(s): December 11, 1997
Received by editor(s) in revised form: April 27, 1998
Published electronically: June 15, 1998
Article copyright: © Copyright 1998 American Mathematical Society