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WHITTAKER FUNCTIONS AND DEMAZURE CHARACTERS

Part of: Lie groups Discontinuous groups and automorphic forms Special aspects of infinite or finite groups

Published online by Cambridge University Press:  22 June 2017

Kyu-Hwan Lee ,
Cristian Lenart  and
Dongwen Liu
Kyu-Hwan Lee
Affiliation:
Department of Mathematics, University of Connecticut, Storrs, CT 06269, USA (khlee@math.uconn.edu)
Cristian Lenart
Affiliation:
Department of Mathematics and Statistics, State University of New York at Albany, Albany, NY 12222, USA (clenart@albany.edu)
Dongwen Liu
Affiliation:
School of Mathematical Science, Zhejiang University, Hangzhou 310027, Zhejiang, PR China (maliu@zju.edu.cn)
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Abstract

In this paper, we consider how to express an Iwahori–Whittaker function through Demazure characters. Under some interesting combinatorial conditions, we obtain an explicit formula and thereby a generalization of the Casselman–Shalika formula. Under the same conditions, we compute the transition matrix between two natural bases for the space of Iwahori fixed vectors of an induced representation of a $p$-adic group; this corrects a result of Bump–Nakasuji.

Keywords

Iwahori–Whittaker functionsCasselman–Shalika formulaDemazure charactersDemazure–Lusztig operatorsshellability

MSC classification

Primary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields
Secondary: 22E50: Representations of Lie and linear algebraic groups over local fields 20F55: Reflection and Coxeter groups
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 18 , Issue 4 , July 2019 , pp. 759 - 781
Copyright
© Cambridge University Press 2017 

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Footnotes

K.-H.L. was partially supported by a grant from the Simons Foundation (#318706). C.L. was partially supported by the NSF grant DMS–1362627. D.L. was partially supported by the Fundamental Research Funds for the Central Universities 2016QNA3002.

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