An archimedean analog of Jacquet - Rallis theorem

Abstract

In this paper we prove that the symmetric pair $(G{L}_{n+k}(F),G{L}_n(F)\times G{L}_k(F))$ is a Gelfand pair for any local field F of characteristic 0. For non-archimedean F it has been proven in [JR]. We use techniques developed in [AG2] to generalize their proof to general local fields.

arXiv comment6 pages. v2,v3: minor changes

References in corpus (3)

• Schwartz functions on Nash manifolds
• (GL(n+1,F),GL(n,F)) is a Gelfand pair for any local field F
• Generalized Harish-Chandra descent and applications to Gelfand pairs

Cited by in corpus (5)

• Periods and nonvanishing of central L-values for GL(2n)
• Generalized Harish-Chandra descent and applications to Gelfand pairs
• Invariant distributions on non-distinguished nilpotent orbits with application to the Gelfand property of (GL(2n,R),Sp(2n,R))
• (GL(2n,C),SP(2n,C)) is a Gelfand Pair
• Uniqueness of Shalika functionals (the Archimedean case)