A topological approach to induction theorems in Springer theory

Treumann, David

doi:10.1090/S1088-4165-09-00342-2

A topological approach to induction theorems in Springer theory
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Represent. Theory 13 (2009), 8-18 Request permission

Abstract:

We give a self-contained account of a construction due to Rossmann, which lifts Springer’s action of a Weyl group on the cohomology of a Springer fiber to an action on its homotopy type. We use this construction to produce a generalization of an “induction theorem” of Alvis and Lusztig, which relates the Springer representations attached to a reductive group to those attached to a Levi subgroup. Our generalization applies to more general centralizers and to representations of Weyl groups on mod $p$ cohomology.

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