A Casselman–Shalika formula for the generalized Shalika model of $\mathrm{SO}_{4n}$

Miyu Suzuki

Vol. 294 (2018), No. 2, 473–494

DOI: 10.2140/pjm.2018.294.473

Abstract

We compute the explicit formula (sometimes called the Casselman–Shalika formula) of the generalized Shalika model for unramified principal series of $p$-adic ${SO}_{4n}$. The method mainly used is the Casselman–Shalika method, modified by Y. Hironaka and applied by Y. Sakellaridis to the case of the Shalika model of ${GL}_{2n}$.

Keywords

Casselman–Shalika formula, Shalika models

Mathematical Subject Classification 2010

Primary: 11F70, 22E50

Secondary: 11F85

Milestones

Received: 20 February 2017

Accepted: 11 November 2017

Published: 20 February 2018