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15 June 2016 Whittaker models and the integral Bernstein center for GLn
David Helm
Duke Math. J. 165(9): 1597-1628 (15 June 2016). DOI: 10.1215/00127094-3450422

Abstract

We establish integral analogues of results of Bushnell and Henniart for spaces of Whittaker functions arising from the groups GLn(F) for F a p-adic field. We apply the resulting theory to the existence of representations arising from the conjectural “local Langlands correspondence in families” and reduce the question of the existence of such representations to a natural conjecture relating the integral Bernstein center of GLn(F) to the deformation theory of Galois representations.

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David Helm. "Whittaker models and the integral Bernstein center for GLn." Duke Math. J. 165 (9) 1597 - 1628, 15 June 2016. https://doi.org/10.1215/00127094-3450422

Information

Received: 5 October 2012; Revised: 20 October 2014; Published: 15 June 2016
First available in Project Euclid: 24 February 2016

zbMATH: 1343.11053
MathSciNet: MR3513570
Digital Object Identifier: 10.1215/00127094-3450422

Subjects:
Primary: 11F70
Secondary: 11F33 , 11S37 , 22E50

Keywords: Bernstein center , deformation theory of Galois representations , local Langlands correspondence , modular representation theory , Whittaker functions

Rights: Copyright © 2016 Duke University Press

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Vol.165 • No. 9 • 15 June 2016
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