The space of degenerate Whittaker models for general linear groups over a finite field

Prasad, Dipendra (2000) The space of degenerate Whittaker models for general linear groups over a finite field International Mathematics Research Notices, 2000 (11). pp. 579-595. ISSN 1073-7928

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Official URL: http://imrn.oxfordjournals.org/content/2000/11/579...

Related URL: http://dx.doi.org/10.1155/S1073792800000313

Abstract

Let G=GL2n(F), where F is a finite field, and P the (n,n) parabolic in G with Levi subgroup GLn(F)×GLn(F) and unipotent radical N=Mn(F). Let ψ0 be a nontrivial additive character ψ0: F→C. Let ψ(X)=ψ0(tr X) be the additive character on N=Mn(F). Let π be an irreducible admissible representation of G. Let πN,ψ, be the largest subspace of π on which N operates via ψ. Since tr(gXg-1=tr(X), it follows that πN,ψ is a representation space for H=ΔGLn(F)→GLn(F)×GLn(F). The space πN,ψ, is referred to as the space of degenerate Whittaker models, or sometimes also as the twisted Jacquet functor of the representation π. The aim of this work is to calculate this for cuspidal representations of GL2n(F).

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ID Code:36158
Deposited On:12 Apr 2011 08:56
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