Geometric approach to parabolic induction

David Kazhdan, Yakov Varshavsky

Published 2015-04-29Version 1

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 the parabolic induction and deduce that a parabolic induction preserves stability. We also give a new (purely geometric) proof that a character of the normalized parabolic induction does not depend on a parabolic subgroup. In the appendix, we use similar argument to extend a theorem of Lusztig-Spaltenstein on induced unipotent classes to all infinite fields.