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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*
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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2006

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