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International Mathematics Research Notices (2000) 2000:579-595, doi:10.1155/S1073792800000313
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Copyright © 2000 Hindawi Publishing Corporation. All rights reserved.

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

Dipendra Prasad

Let Formula, where Formula is a finite field, and P the (n,n) parabolic in G with Levi subgroup Formula and unipotent radical Formula. Let {psi}0 be a nontrivial additive character Formula. Let Formula be the additive character on Formula. Let {pi} be an irreducible admissible representation of G. Let {pi}N,{psi}, be the largest subspace of {pi} on which N operates via {psi}. Since Formula, it follows that {pi}N,{psi} is a representation space for Formula. The space {pi}N,{psi}, is referred to as the space of degenerate Whittaker models, or sometimes also as the twisted Jacquet functor of the representation {pi}. The aim of this work is to calculate this for cuspidal representations of Formula.


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