In their paper "Uniqueness of linear periods", Compositio Mathematica, $\textbf{102}$ (1996), 65-123, Jacquet and Rallis asked the following question in the middle of page 67.

Let $F$ be a $p$-adic field, and $n$ be a positive integer. Let $H_0=\left\{\begin{pmatrix}a&\\ &a \end{pmatrix},a\in GL_n(F)\right\}\subset GL_{2n}(F)$.

Given an irreducible smooth representation of $GL_{2n}(F)$, if $\textrm{Hom}_{H_0}(\pi,1)\ne 0$, could we conclude that $\pi$ is self-contragredient?

If $n=1$, it is well-known that the answer is yes. How about the general case? What is the current status of this problem?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.