English

Linear periods for unitary representations

Representation Theory 2022-09-22 v2

Abstract

Let FF be a local non-Archimedean field of characteristic zero with a finite residue field. Based on Tadi\'{c}'s classification of the unitary dual of GL2n(F)\mathrm{GL}_{2n}(F), we classify irreducible unitary representations of GL2n(F)\mathrm{GL}_{2n}(F) that have nonzero linear periods, in terms of Speh representations that have nonzero periods. We also give a necessary and sufficient condition for the existence of a nonzero linear period for a Speh representation.

Keywords

Cite

@article{arxiv.2007.11763,
  title  = {Linear periods for unitary representations},
  author = {Chang Yang},
  journal= {arXiv preprint arXiv:2007.11763},
  year   = {2022}
}

Comments

34 pages, 2 figures. Comments are welcome! Fix some errors (those related to Lemma 3.1 (2) in the first version). Final version to appear in Math Z

R2 v1 2026-06-23T17:20:03.721Z