The $\mathrm{SL}_1(D)$-distinction problem

Hengfei Lu

Vol. 300 (2019), No. 1, 65–82

DOI: 10.2140/pjm.2019.300.65

Abstract

We use the local theta correspondences between the quaternionic Hermitian groups and the quaternionic skew-Hermitian groups to understand the distinction problem for the symmetric pair ${SL}_2\left(E\right)∕{SL}_1\left(D\right)$, where $E$ is a quadratic field extension of a nonarchimedean local field $F$ and $D$ is a $4$-dimensional division quaternion algebra over $F$.

Keywords

theta lift, distinction problem, division quaternion algebra

Mathematical Subject Classification 2010

Primary: 11F27

Secondary: 22E50

Milestones

Received: 6 May 2018

Revised: 12 September 2018

Accepted: 12 September 2018

Published: 20 July 2019