The dimension formula for certain twisted Jacquet modules of a cuspidal representation of GL(n,Fq)

Let n≥2 be a positive integer. Let F be the finite field of order q and G=GL(n,F). Let P=MN be the standard parabolic subgroup of G corresponding to the partition (k,n−k). Let A∈M((n−k)×k,F) be a rank t matrix. In this paper, we compute the dimension formula for the twisted Jacquet module πN,ψA that...

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Bibliographic Details
Published in:Linear algebra and its applications Vol. 710; pp. 151 - 164
Main Authors: Balasubramanian, Kumar, Khurana, Himanshi
Format: Journal Article
Language:English
Published: Elsevier Inc 01.04.2025
Subjects:
Cuspidal representations
Dimension formula
Twisted Jacquet module
Cuspidal representations
Twisted Jacquet module
Dimension formula
primary
ISSN:0024-3795
Online Access:Get full text
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Summary:Let n≥2 be a positive integer. Let F be the finite field of order q and G=GL(n,F). Let P=MN be the standard parabolic subgroup of G corresponding to the partition (k,n−k). Let A∈M((n−k)×k,F) be a rank t matrix. In this paper, we compute the dimension formula for the twisted Jacquet module πN,ψA that depends on n,k and t, when π is an irreducible cuspidal representation of G and ψA is a character of N associated with A.
ISSN:0024-3795
DOI:10.1016/j.laa.2025.01.027