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Representation Theory

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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
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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Meinolf Geck
Affiliation: Institut Girard Desargues, bat. 101, Université Lyon 1, 43 bd du 11 novembre 1918, F–69622 Villeurbanne cedex, France

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