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
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 SL2(E)∕SL1(D), where E is a quadratic field extension of a nonarchimedean local field F and D is a 4-dimensional division quaternion algebra over F.

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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
Authors
Hengfei Lu
School of Mathematics
Tata Institute of Fundamental Research
Colaba, Mumbai
India		 Weizmann Institute of Science
Rehovot
Israel