A Casselman-Shalika formula for the shalika model of GLn

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Abstract

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 GLn, 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.

Original languageEnglish (US)
Pages (from-to)1095-1120
Number of pages26
JournalCanadian Journal of Mathematics
Volume58
Issue number5
DOIs
StatePublished - Oct 2006
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Casselman-Shalika
  • Gelfand pairs
  • Periods
  • Shalika model
  • Spherical functions

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