Local newforms for the general linear groups over a nonarchimedean local field
Abstract
In [12], JacquetPiatetskiiShapiroShalika 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 RankinSelberg integrals for Speh representations.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.09070
 Bibcode:
 2021arXiv211009070A
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Representation Theory
 EPrint:
 58 pages