The \(\operatorname{SL}_1(D)\)-distinction problem. (English) Zbl 1457.11040
Summary: 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 \(\operatorname{SL}_2(E)/\operatorname{SL}_1(D)\), where \(E\) is a quadratic field extension of a nonarchimedean local field \(F\) and \(D\) is a 4-dimensional division quaternion algebra over \(F\).
MSC:
| 11F27 | Theta series; Weil representation; theta correspondences |
| 22E50 | Representations of Lie and linear algebraic groups over local fields |
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