English

On the Jacquet functor of Symplectic groups

Representation Theory 2024-05-13 v1

Abstract

Let \F\F be a non-Archimedean local field.~Consider \Gn:=\Sp2n(\F)\G_{n}:= \Sp_{2n}(\F) and let \M:=\GLl×\Gnl\M:= \GL_l \times \G_{n-l} be a maximal Levi subgroup of \Gn\G_{n}.~This paper undertakes the computation of the Jacquet module of representations of \Gn\G_{n} with respect to the maximal Levi subgroup, belonging to a particular class. Finally, we conclude that for a subclass of representations of \Gn,\G_{n}, multiplicity of the Jacquet module does not exceed 2.

Keywords

Cite

@article{arxiv.2405.06450,
  title  = {On the Jacquet functor of Symplectic groups},
  author = {Prem Dagar and Mahendra Kumar Verma},
  journal= {arXiv preprint arXiv:2405.06450},
  year   = {2024}
}

Comments

12 pages; comments are welcome. arXiv admin note: text overlap with arXiv:2405.05719