3 problems

Let $\pi_V\in\Pi_{\mathrm{CW}}(\operatorname{SO}(V))$ and $\pi_W\in\Pi_{\mathrm{CW}}(\operatorname{SO}(W))$. Let $X^+$ be the space defining $\operatorname{GL}(X^+)$, and let…

Let $(W,V)$ be an admissible pair. Let $\pi_V\in \Pi_{\mathrm{CW}}(\operatorname{SO}(V))$ and $\pi_W\in \Pi_{\mathrm{CW}}(\operatorname{SO}(W))$, possibly reducible, and suppose th…

Let $(G,H,\xi)$ be a Gross–Prasad triple attached to an admissible pair $(W,V)$ over $F$. For a generic local $L$-parameter $\varphi$ of $G$, let…