Modular principal series representations

2006/03/02 by Geck, Meinolf
#20C08 #20C33 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.math/0603046

Abstract

Recently, there has been considerable progress in classifying the irreducible representations of Iwahori--Hecke algebras at roots of unity. Here, we present an application of these results to ℓ-modular Harish--Chandra series for a finite group of Lie type G(q). Under some mild condition on ℓ, we show that the ℓ-modular principal series representations of G(q) are naturally parametrized by a \em subset of the set of complex irreducible characters of the Weyl group of G(q). We also show that this subset is ``generic'' in a precise sense.

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