Local Rankin-Selberg integrals for SpehA representations

Erez M. Lapid, Zhengyu Mao

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We construct analogues of Rankin-Selberg integrals for Speh representations of the general linear group over a -adic field. The integrals are in terms of the (extended) Shalika model and are expected to be the local counterparts of (suitably regularized) global integrals involving square-integrable automorphic forms and Eisenstein series on the general linear group over a global field. We relate the local integrals to the classical ones studied by Jacquet, Piatetski-Shapiro and Shalika. We also introduce a unitary structure for Speh representation on the Shalika model, as well as various other models including Zelevinsky's degenerate Whittaker model.

Original languageEnglish (US)
Pages (from-to)908-945
Number of pages38
JournalCompositio Mathematica
Volume156
Issue number5
DOIs
StatePublished - May 1 2020

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Keywords

  • 2010 Mathematics Subject Classification11F70

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