The dimension formula for certain twisted Jacquet modules of a cuspidal representation of GL(n,Fq) - Balasubramanian, Kumar; Khurana, Himanshi (Linear algebra and its applications, 2025)
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.