On disjointness of linear models and degenerate Whittaker models

Eitan Sayag, Mahendra Kumar Verma

Research output: Contribution to journalArticlepeer-review

Abstract

In this article we reprove and generalize a result of N. Matringe [12] concerning generic representations of GLn(F) that admits a linear model with respect to a maximal Levi subgroup GLp(F)×GLq(F), where F is a non-archimedean field. He showed that in this case |p−q|≤1. We extend this result to the case where F is a finite field or a local field of characteristic different from 2. Further, we study non-generic representations of GLn(F) and describe their possible linear models in terms of their rank r(π) (see Section 6). Our arguments are based on the method of Gelfand-Kazhdan and the theory of distribution and provide uniform proofs for finite, p-adic and archimedean fields.

Original languageEnglish
Pages (from-to)56-82
Number of pages27
JournalJournal of Number Theory
Volume207
DOIs
StatePublished - 1 Feb 2020

Keywords

  • Degenerate Whittaker models
  • Disjointness
  • Linear models

ASJC Scopus subject areas

  • Algebra and Number Theory

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