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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Left cells and constructible representations
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by Meinolf Geck
Represent. Theory 9 (2005), 385-416
Published electronically: May 2, 2005

Erratum: Represent. Theory 11 (2007), 172-173.


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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Bibliographic 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
  • Email:
  • Received by editor(s): May 10, 2004
  • Received by editor(s) in revised form: March 26, 2005
  • Published electronically: May 2, 2005
  • © Copyright 2005 American Mathematical Society
  • Journal: Represent. Theory 9 (2005), 385-416
  • MSC (2000): Primary 20C08
  • DOI:
  • MathSciNet review: 2133765