In this paper we prove a conjecture of Jacquet about supercuspidal representations of GLn(K) distinguished by GLn(k), or by Un(k), for K a quadratic unramified extension of a non-Archimedean local field k.
Dipendra Prasad. "On a conjecture of Jacquet about distinguished representations of GL(n)." Duke Math. J. 109 (1) 67 - 78, 15 July 2001. https://doi.org/10.1215/S0012-7094-01-10912-5