#### Vol. 294, No. 2, 2018

 Recent Issues Vol. 295: 1 Vol. 294: 1  2 Vol. 293: 1  2 Vol. 292: 1  2 Vol. 291: 1  2 Vol. 290: 1  2 Vol. 289: 1  2 Vol. 288: 1  2 Online Archive Volume: Issue:
 The Journal Subscriptions Editorial Board Officers Special Issues Submission Guidelines Submission Form Contacts Author Index To Appear ISSN: 0030-8730
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