Murnaghan-Kirillov theory for depth-zero supercuspidal representations: Reduction to Lusztig functions

Stephen Debacker*, David Kazhdan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The goal of Murnaghan-Kirillov theory is to associate to an irreducible smooth representation of a reductive p-adic group a family of regular semisimple orbital integrals in the Lie algebra with the following property: the character of π is given, on a well determined set, by an explicit combination of the Fourier transforms of these orbital integrals. Subject to certain restrictions, we adapt arguments of Waldspurger to show that, for depth-zero irreducible smooth supercuspidal representations, this problem may be reduced to a similar one for distributions associated to Lusztig functions.

Original languageEnglish
Pages (from-to)737-766
Number of pages30
JournalTransformation Groups
Volume16
Issue number3
DOIs
StatePublished - Sep 2011

Keywords

  • character
  • depth-zero
  • Harmonic analysis
  • reductive p-adic group
  • representation
  • supercuspidal

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