9 problems

Let $\psi\in\Psi({}^{\vee}G^{\Gamma})$ be an Arthur parameter, let $\varphi_\psi$ be its associated Langlands parameter, and let $\Pi(G)_\varphi$ denote the corresponding $L$-packe…

Salamanca-Riba–Vogan's convex-hull conjecture. If $X$ is unitary, then $\Lambda$ must lie in

Salamanca-Riba–Vogan's unitarity conjecture. The above bijection preserves unitarity.

Let $G_{\mathbb R}$ be a real reductive group, let $\widetilde{\mathcal O}$ be a birationally rigid nilpotent cover for its complexification, and let $\mathcal O_{\theta}$ be a $K$…

Let $G_{\mathbb R}$ be the real points of a connected reductive algebraic group, and let $\mathsf{Cov}^{i\mathbb R}(G_{\mathbb R})$ denote the real co-adjoint covers of…

Let $G$ be an equal-rank real reductive group with maximal compact subgroup $K$, and let $\widetilde K$ be the spin double cover of $K$. For an irreducible unitary…

Low-rank reduction conjecture. An irreducible admissible representation $\pi$ of $\operatorname{GL}_n({\mathbb R})$ occurs as a Jordan–Hölder factor of $Ps(\underline{\pi})$ if and…

Let $G$ be a real reductive group, and let $St_G$ denote the Steinberg representation of $G({\mathbb R})$. Let $D_2: W_{\mathbb R}\rightarrow \operatorname{SL}_2({\mathbb C})$ be t…

Let $G$ be a reductive group, let $\delta_0$ be the specified automorphism, and let $\xi$ be a strong involution for $G$ with dominant regular integral infinitesimal cocharacter…