2024/01/30 by Sanjeev Kumar Pandey, Pandey, Sanjeev Kumar, C. G. Venketasubramanian +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research
paper · pdf · doi:10.48550/arxiv.2401.16933
Let F be a non-archimedean local field. For the symplectic group Sp4(F), let P and Q denote respectively its Siegel and Klingen parabolic subgroups with respective Levi decompositions P=MN and Q=LU. For a non-trivial character ψ of the unipotent radical N of P, let Mψ denote the stabilizer of the character ψ in M under the conjugation action of M on characters of N. For an irreducible representation of the Levi subgroups M or L, let π denote the respective representation of Sp4(F) parabolically induced either from P or from Q. Let ψ be a character of the group N given by a rank one quadratic form. In this article, we determine the structure of the twisted Jacquet module rN,ψ(π) as an Mψ-module. We also deduce the analogous results in the case where F is a finite field of order q.