The SL(1,D)-distinction problem

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,E)/SL(1,D), where E is a quadratic field extension of a nonarchimedean local field extension F and D is a 4-dimensional division quaternion algebra over F

arXiv comment11 pages. arXiv admin note: text overlap with arXiv:1802.01941