A Casselman–Shalika Formula for the Shalika Model of GL n

Sakellaridis, Yiannis

Canadian journal of mathematics, Tome 58 (2006) no. 5, pp. 1095-1120

Résumé

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.

Détail

DOI : 10.4153/CJM-2006-040-6

Mots-clés : 22E50, 11F70, 11F85, Casselman–Shalika, periods, Shalika model, spherical functions, Gelfand pairs

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