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On the representation theory of Iwahori-Hecke algebras of extended finite Weyl groups


Author: Meinolf Geck
Journal: Represent. Theory 4 (2000), 370-397
MSC (2000): Primary 20C08; Secondary 20C20
DOI: https://doi.org/10.1090/S1088-4165-00-00093-5
Published electronically: September 11, 2000
MathSciNet review: 1780716
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Abstract: 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: geck@desargues.univ-lyon1.fr

Received by editor(s): January 19, 2000
Received by editor(s) in revised form: August 7, 2000
Published electronically: September 11, 2000
Article copyright: © Copyright 2000 American Mathematical Society