On representations of ${\rm GL}_{2n}(F)$ with a symplectic period

Arnab Mitra

On representations of ${\rm GL}_{2n}(F)$ with a symplectic period

Representation Theory 2016-01-15 v1

Authors: Arnab Mitra

Abstract

The main aim of this paper is to classify the irreducible admissible representations of ${\rm GL}_{4}(F)$ and ${\rm GL}_{6}(F)$ for a nonarchimedean local field $F$ , which bear a nontrivial linear form invariant under the groups ${\rm Sp}_{4}(F)$ and ${\rm Sp}_{6}(F)$ respectively. We propose a few conjectures for the general case.

Keywords

representations of GL_{2n}(F) symplectic period irreducible admissible representations nonarchimedean local field Sp_{2n}(F) invariant linear form classification

Cite

@article{arxiv.1601.03611,
  title  = {On representations of ${\rm GL}_{2n}(F)$ with a symplectic period},
  author = {Arnab Mitra},
  journal= {arXiv preprint arXiv:1601.03611},
  year   = {2016}
}

Comments

Published in Pacific Journal of Mathematics

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