8 problems

Let $\tilde{\varphi}_0:X_{Q,n}/X_{Q,n}^{sc}\to X/X_G^{sc}$ be well-defined, let $\mathfrak{w}=(B,U,\psi)$ be Whittaker data, and let…

Assume that $\rho$ has Loewy length $3$. Let $\rho$ be a representation for which $\rho$-compatible representations $\Pi(\rho)$ and $\Pi(\rho)^{\mathrm{ord}}$ are defined, with…

Archimedean co-socle analogy conjecture. The length of the maximal semi-simple quotient of $\operatorname{I}_{P,v_1}(s,\mathbf{1})$ equals that of…

Let $\tilde{G}$ be a persistent $n$-fold cover, and let $\nu\in X\otimes\mathbf{R}$ be regular with $\Phi(\nu)\subset\Delta$. For $S\subset\Phi(\nu)$, let $W(S)$ be the Weyl subgro…

Pole–reducibility conjecture. In the right complex half-plane, a degenerate Eisenstein series has a pole if and only if the corresponding local degenerate principal series is reduc…

Let $\rho:{\operatorname{Gal}}({\overline{\mathbb Q}}_p/{\mathbb Q}_p)\longrightarrow \widehat{B}_{C_\rho}(E)\subseteq\widehat{G}(E)$ be generic, with $C_\rho\subseteq R^{+\vee}$ c…

Let $G$ be a split reductive group over ${\mathbb Q}_p$, with negative Borel subgroup $B^-({\mathbb Q}_p)$, torus $T({\mathbb Q}_p)$, and set of simple roots $S$. Let…

Let $\bmu$ be a parabolic character, let $L$ be the associated Levi subgroup, and let $\Pi^c$, $\sW^c$, and $\sH^c$ be the corresponding principal-series family, induced representa…