On Iwahori–Whittaker functions for metaplectic groups

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jun 2017Embargo end date: 01 Jan 2015 English Publisher:Elsevier BVJournal:Advances in Mathematics, volume 313, pages 875-914 (issn: 0001-8708,

Copyright policy )Funded by:NSERC | unidentified

Authors: Patnaik, Manish; Puskás, Anna;

doi: 10.1016/j.aim.2017.04.005 , 10.48550/arxiv.1509.01594

arXiv: 1509.01594

On Iwahori–Whittaker functions for metaplectic groups

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Abstract

We relate Iwahori-Whittaker functions on metaplectic covers to certain Demazure-Lusztig operators, the latter of which are built from a Weyl group action previously considered by G. Chinta and P. Gunnells. Using a certain combinatorial identity for the sum of these Demazure-Lusztig operators, we obtain an analogue of the Casselman-Shalika formula for spherical Whittaker functions in this context.

Previous version had title "On the Casselman-Shalika formula for metaplectic groups"

Related Organizations

University of Alberta
Canada

Keywords

Whittaker functions, Mathematics - Number Theory, Demazure-Lusztig operators, metaplectic cover, Analysis on \(p\)-adic Lie groups, Iwahori-Whittaker functions, spherical Whittaker functions, Casselman-Shalika formula, Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\), FOS: Mathematics, Number Theory (math.NT), Representation Theory (math.RT), Mathematics - Representation Theory

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