Vol. 294, No. 2, 2018

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

Miyu Suzuki

Vol. 294 (2018), No. 2, 473–494
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