Journal title
Mathematische Zeitschrift
DOI
10.1007/s00209-018-2097-y
Issue
1-2
Volume
291
Last updated
2024-04-08T05:16:22.937+01:00
Page
609-633
Abstract
Let π be an irreducible cuspidal representation of GLkn(Fq). Assume that π=πθ, corresponds to a regular character θ of F∗qkn. We consider the twisted Jacquet module of π with respect to a non-degenerate character of the unipotent radical corresponding to the partition (nk) of kn. We show that, as a GLn(Fq)-representation, this Jacquet module is isomorphic to πθ↾F∗n⊗Stk−1, where St is the Steinberg representation of GLn(Fq). This generalizes a theorem of D. Prasad, who considered the case k=2. We prove and rely heavily on a formidable identity involving q-hypergeometric series and linear algebra.
Symplectic ID
1145836
Submitted to ORA
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Publication type
Journal Article
Publication date
05 Jun 2018