A Casselman-Shalika formula for the Shalika model of GL_n

Details A Casselman-Shalika formula for the Shalika model of GL_n A Casselman-Shalika formula for the Shalika model of GL_n

2006-06-06

arxiv.org/abs/math/0606129v1

Mathematics

Representation Theory

23 pages. Accepted for publication in the Canadian Journal of Mathematics

Scientific paper

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 GL_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.

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