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arXiv · 1504.07859

Geometric approach to parabolic induction

David Kazhdan·Yakov Varshavsky
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Abstract

In this note we construct a "restriction" map from the cocenter of a reductive group G over a local non-archimedean field F to the cocenter of a Levi subgroup. We show that the dual map corresponds to parabolic induction and deduce that parabolic induction preserves stability. We also give a new (purely geometric) proof that the character of normalized parabolic induction does not depend on a parabolic subgroup. In the appendix, we use a similar argument to extend a theorem of Lusztig-Spaltenstein on induced unipotent classes to all infinite fields.

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David Kazhdan, Yakov Varshavsky. 2015-04-29. Geometric approach to parabolic induction. https://arxiv.org/abs/1504.07859

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