#### Vol. 300, No. 1, 2019

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

### Hengfei Lu

Vol. 300 (2019), No. 1, 65–82
##### 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
Primary: 11F27
Secondary: 22E50
##### Milestones
Received: 6 May 2018
Revised: 12 September 2018
Accepted: 12 September 2018
Published: 20 July 2019
##### Authors
 Hengfei Lu School of Mathematics Tata Institute of Fundamental Research Colaba, Mumbai India Weizmann Institute of Science Rehovot Israel