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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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On the representation theory of Iwahori-Hecke algebras of extended finite Weyl groups
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by Meinolf Geck PDF
Represent. Theory 4 (2000), 370-397 Request permission


We apply Lusztig’s theory of cells and asymptotic algebras to the Iwahori–Hecke algebra of a finite Weyl group extended by a group of graph automorphisms. This yields general results about splitting fields (extending earlier results by Digne–Michel) and decomposition matrices (generalizing earlier results by the author). Our main application is to establish an explicit formula for the number of simple modules in type $D_n$ (except in characteristic $2$), using the known results about type $B_n$ due to Dipper, James, and Murphy and Ariki and Mathas.
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Additional Information
  • Meinolf Geck
  • Affiliation: Institut Girard Desargues, bat. 101, Université Lyon 1, 43 bd du 11 novembre 1918, F–69622 Villeurbanne cedex, France
  • MR Author ID: 272405
  • Email:
  • Received by editor(s): January 19, 2000
  • Received by editor(s) in revised form: August 7, 2000
  • Published electronically: September 11, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Represent. Theory 4 (2000), 370-397
  • MSC (2000): Primary 20C08; Secondary 20C20
  • DOI:
  • MathSciNet review: 1780716