Modular principal series representations

Details Modular principal series representations Modular principal series representations

2006-03-02

arxiv.org/abs/math/0603046v3

Mathematics

Representation Theory

16 pages; the revised version contains additional references; the second revision corrects minor errors; to appear in IMRN (20

Scientific paper

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 $\ell$-modular Harish--Chandra series for a finite group of Lie type $G(q)$. Under some mild condition on $\ell$, we show that the $\ell$-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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