8 problems

Let $G=\mathrm G(F)$, where $\mathrm G$ is a connected reductive algebraic group defined over $F$ and inner to a split group. Let ${}^{K}\mathrm{WF}(\pi)$ denote the unramified can…

Let $U(p,q)$ be a real unitary group, and let a special unipotent representation mean a representation in the special-unipotent class considered in the paper. A representation is f…

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 $K$…

Cuspidality conjecture. Then $p$ is $\tau_d$-cuspidal.

Unipotent-family conjecture. There exists a unique bijection

Let $G$ be a simple $F$-split group. Let ${\mathcal R}^p_{{\mathrm{un}},{\mathrm{ell}}}(G)$ be the elliptic unipotent representation space, let…

Let $\mathfrak{g}$ be the Lie algebra of a complex semisimple Lie group. Let $\mathcal{O}$ be a special nilpotent orbit, let $\overline{A}(\mathcal{O})$ be its Lusztig quotient, an…

Kernel $n$-unipotent conjecture. For every integer $n\geq 3$, the group $G_F(p)$ has the kernel $n$-unipotent property.