Representations of reductive groups distinguished by symmetric subgroups

Itay Glazer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let G be a complex connected reductive group, Gθ be its fixed point subgroup under a Galois involution θ and H be an open subgroup of Gθ. We show that any H-distinguished representation π satisfies:(1)πθ≃ π~ , where π~ is the contragredient representation and πθ is the twist of π under θ.(2)dimC(π∗)H≤|B\G/H|, where B is a Borel subgroup of G. By proving the first statement, we give a partial answer to a conjecture by Prasad and Lapid.

Original languageEnglish (US)
Pages (from-to)471-489
Number of pages19
JournalMathematische Zeitschrift
Volume289
Issue number1-2
DOIs
StatePublished - Jun 1 2018
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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