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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Left cells and constructible representations
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by Meinolf Geck PDF
Represent. Theory 9 (2005), 385-416 Request permission

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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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
  • 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