Geometric approach to parabolic induction

David Kazhdan, Yakov Varshavsky*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In this paper 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 the 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. We also prove a group version of a theorem of Harish-Chandra about the density of the span of regular semisimple orbital integrals.

Original languageAmerican English
Pages (from-to)2243-2269
Number of pages27
JournalSelecta Mathematica, New Series
Volume22
Issue number4
DOIs
StatePublished - 1 Oct 2016

Bibliographical note

Publisher Copyright:
© 2016, Springer International Publishing.

Keywords

  • 22E50 (22E35)

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