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Representation Theory
Representation Theory
ISSN 1088-4165

 

Left cells and constructible representations


Author: Meinolf Geck
Journal: Represent. Theory 9 (2005), 385-416
MSC (2000): Primary 20C08
Published electronically: May 2, 2005
Erratum: Represent. Theory 11 (2007), 272-273
MathSciNet review: 2133765
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Abstract: We consider the partition of a finite Coxeter group $W$ into left cells with respect to a weight function $L$. In the equal parameter case, Lusztig has shown that the representations carried by the left cells are precisely the so-called constructible ones. We show that this holds for general $L$, assuming that the conjectural properties (P1)-(P15) in Lusztig's book on Hecke algebras with unequal parameters hold for $W,L$. Our proofs use the idea (Gyoja, Rouquier) that left cell representations are projective in the sense of modular representation theory. This also gives partly new proofs for Lusztig's result in the equal parameter case.


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Additional Information

Meinolf Geck
Affiliation: Institut Girard Desargues, bat. Jean Braconnier, Université Lyon 1, 21 av Claude Bernard, F–69622 Villeurbanne Cedex, France
Email: geck@igd.univ-lyon1.fr

DOI: http://dx.doi.org/10.1090/S1088-4165-05-00245-1
PII: S 1088-4165(05)00245-1
Received by editor(s): May 10, 2004
Received by editor(s) in revised form: March 26, 2005
Published electronically: May 2, 2005
Article copyright: © Copyright 2005 American Mathematical Society