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arXiv · 1304.2642

Weyl group actions on the Springer sheaf

Pramod N. Achar·Anthony Henderson·Daniel Juteau·Simon Riche
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Abstract

We show that two Weyl group actions on the Springer sheaf with arbitrary coefficients, one defined by Fourier transform and one by restriction, agree up to a twist by the sign character. This generalizes a familiar result from the setting of l-adic cohomology, making it applicable to modular representation theory. We use the Weyl group actions to define a Springer correspondence in this generality, and identify the zero weight spaces of small representations in terms of this Springer correspondence.

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Pramod N. Achar, Anthony Henderson, Daniel Juteau, Simon Riche. 2013-10-03. Weyl group actions on the Springer sheaf. https://doi.org/10.1112/plms%2Fpdt055

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