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 language | American English |
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Pages (from-to) | 2243-2269 |
Number of pages | 27 |
Journal | Selecta Mathematica, New Series |
Volume | 22 |
Issue number | 4 |
DOIs | |
State | Published - 1 Oct 2016 |
Bibliographical note
Publisher Copyright:© 2016, Springer International Publishing.
Keywords
- 22E50 (22E35)