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

Geck, Meinolf

doi:10.1090/S1088-4165-00-00093-5

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

Represent. Theory 4 (2000), 370-397

DOI: https://doi.org/10.1090/S1088-4165-00-00093-5

Published electronically: September 11, 2000

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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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