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A Casselman–Shalika Formula for the Shalika Model of GLn

Published online by Cambridge University Press:  20 November 2018

Yiannis Sakellaridis
Yiannis Sakellaridis*
Affiliation:
Department of Mathematics, Stanford University, Stanford, CA 94305-2125, U.S.A. e-mail: yiannis@math.stanford.edu
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Abstract

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The Casselman–Shalika method is a way to compute explicit formulas for periods of irreducible unramified representations of $p$-adic groups that are associated to unique models (i.e., multiplicity-free induced representations). We apply this method to the case of the Shalika model of $\text{G}{{\text{L}}_{n}}$, which is known to distinguish lifts from odd orthogonal groups. In the course of our proof, we further develop a variant of the method, that was introduced by Y.Hironaka, and in effect reduce many such problems to straightforward calculations on the group.

Keywords

22E5011F7011F85Casselman–ShalikaperiodsShalika modelspherical functionsGelfand pairs
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 58 , Issue 5 , 01 October 2006 , pp. 1095 - 1120
Copyright
Copyright © Canadian Mathematical Society 2006

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