Bernstein components via the Bernstein center

Alexander Braverman, David Kazhdan

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Let G be a reductive p-adic group. Let Φ be an invariant distribution on G lying in the Bernstein center Z(G). We prove that Φ is supported on compact elements in G if and only if it defines a constant function on every component of the set Irr (G) ; in particular, we show that the space of all elements of Z(G) supported on compact elements is a subalgebra of Z(G). Our proof is a slight modification of the argument from Section 2 of Dat (J Reine Angew Math 554:69–103, 2003), where our result is proved in one direction.

Original languageEnglish
Pages (from-to)2313-2323
Number of pages11
JournalSelecta Mathematica, New Series
Volume22
Issue number4
DOIs
Publication statusPublished - 1 Oct 2016
Externally publishedYes

Keywords

  • 20G05
  • 20G25
  • 22E35
  • 22E50

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