A topological approach to induction theorems in Springer theory

Details A topological approach to induction theorems in Springer theory A topological approach to induction theorems in Springer theory

2008-09-16

arxiv.org/abs/0809.2801v1

Mathematics

Representation Theory

11 pages

Scientific paper

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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