8 problems

Aubert–Zelevinsky duality conjecture. If $X=X(q^{\frac{1}{2}{\it h}},\mathcal{S},\mathcal{L})$ is an irreducible unipotent representation in…

Let $G$ be a reductive group and let $\check G$ be its Langlands dual group. Denote by $\mathcal{H}_G^{dR}$ and $\mathcal{H}_{\check G}^{dR}$ the de Rham potent Hecke monads, and b…

Let $n$ be an even integer. An elementary wild character variety is a wild character variety arising from an elementary connection, considered up to isomorphism. Finiteness conject…

Let $W$ be an irreducible spetsial complex reflection group, and write $\operatorname{Irr}(W)$ for its irreducible characters. Let $\operatorname{Deg}_\chi(q)$ and…

Let $G$ be a possibly disconnected reductive group, let $\mathcal N_G$ be its nilpotent cone, and let $\mathcal O$ be a nilpotent orbit. If…

Let $(G,V)$ be a visible stable polar representation for a connected reductive group $G$. Let $\pi\colon V\to V/\!/G$ be the quotient map, let $P$ be its nearby cycles sheaf, let…

Let $G$ be the reductive $p$-adic group and let $\mathsf{R}_{\mathsf{un},\mathsf{ell}}$ denote its elliptic unipotent representation space. Let…

Fourier decomposition conjecture. There exists such an $L$ inducing a canonical splitting