Scholarlink

<p>It is well-known (cf. Weil, Gérardin’s works) that there are two different Weil representations of a symplectic group over an odd finite field. By a twisted action, we show that they can be reorganized into a representation of a projective symplectic similitude group. We also discuss the even field case by following Genestier–Lysenko and Gurevich–Hadani’s works on geometric Weil representations in characteristic two. As a result, we approach some of their results from the lattice model, which is inspired by Mœglin–Vignéras–Waldspurger, Prasad and Takeda’s works.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Extended Weil representations: the finite field cases

  • 期刊论文

  • 发表日期：

    2025年1月31日

查看全文
  • Chun-Hui Wang

摘要

It is well-known (cf. Weil, Gérardin’s works) that there are two different Weil representations of a symplectic group over an odd finite field. By a twisted action, we show that they can be reorganized into a representation of a projective symplectic similitude group. We also discuss the even field case by following Genestier–Lysenko and Gurevich–Hadani’s works on geometric Weil representations in characteristic two. As a result, we approach some of their results from the lattice model, which is inspired by Mœglin–Vignéras–Waldspurger, Prasad and Takeda’s works.