Remote Access Representation Theory
Green Open Access

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), 172-173.
MathSciNet review: 2133765
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2000): 20C08

Retrieve articles in all journals with MSC (2000): 20C08

Additional Information

Meinolf Geck
Affiliation: Institut Girard Desargues, bat. Jean Braconnier, Université Lyon 1, 21 av Claude Bernard, F–69622 Villeurbanne Cedex, France
MR Author ID: 272405

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