Local newforms for the general linear groups over a non-archimedean local field

Atobe H., KONDO S., Yasuda S.

FORUM OF MATHEMATICS PI, vol.10, 2022 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10
  • Publication Date: 2022
  • Doi Number: 10.1017/fmp.2022.17
  • Journal Name: FORUM OF MATHEMATICS PI
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Middle East Technical University Northern Cyprus Campus Affiliated: Yes

Abstract

In [14], Jacquet-Piatetskii-Shapiro-Shalika defined a family of compact open subgroups of p-adic general linear groups indexed by nonnegative integers and established the theory of local newforms for irreducible generic representations. In this paper, we extend their results to all irreducible representations. To do this, we define a new family of compact open subgroups indexed by certain tuples of nonnegative integers. For the proof, we introduce the Rankin-Selberg integrals for Speh representations.