An archimedean analog of Jacquet - Rallis theorem

Avraham Aizenbud; Dmitry Gourevitch

An archimedean analog of Jacquet - Rallis theorem

Representation Theory 2008-05-15 v3

Authors: Avraham Aizenbud , Dmitry Gourevitch

Abstract

In this paper we prove that the symmetric pair $(GL_{n+k}(F),GL_n(F) \times GL_k(F))$ 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.

Keywords

jacquet-rallis theorem gelfand pairs symmetric pairs local fields archimedean analog general linear groups

Cite

@article{arxiv.0803.3397,
  title  = {An archimedean analog of Jacquet - Rallis theorem},
  author = {Avraham Aizenbud and Dmitry Gourevitch},
  journal= {arXiv preprint arXiv:0803.3397},
  year   = {2008}
}

Comments

6 pages. v2,v3: minor changes

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