2 problems

Let $G$ and $G'$ be inner forms, and let $\phi$ and $\phi'$ be automorphisms arising from the corresponding adjoint groups. Suppose they correspond under the natural isomorphism of…

Let $E/F$ be the quadratic extension, let $G'=\operatorname{GL}_{2n}$, and let $\pi'$ be a cuspidal representation of $G'(\mathbf A)$. For each $D\in X(E:F:\pi')$, let $\pi_D$ be t…