5 problems

Kaletha's internal parametrization conjecture. The packet on $(G',\iota,z)$ should be internally labeled by

Let $G$ be a reductive group, let $Z$ be the relevant central subgroup, and let $\Pi^{\operatorname{rig},Z}(G)$ and \Phi_\operatorname{e}^Z({}^LG) denote the representation and e…

Arthur–Vogan packet branching conjecture. Suppose that $\underline G$ and $\underline{G}^1$ are a relevant pair. Then the restriction and branching behavior predicted for the corre…

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…