5 problems

The exactness conjecture. The functor $\mathrm F_{G,\underline{\lambda}}$ is exact.

Let $G$ be a reductive group over $\mathbb F_q$, let $\rho$ be a representation as in the Braverman–Kazhdan construction, and let $\Phi_{G,\rho,\psi}$ be the corresponding $\rho$-B…

Braverman–Kazhdan's conjecture. The functor $\mathrm F_{G,\rho}$ is exact with respect to the perverse $t$-structure, and it commutes with induction functors. This conjecture conce…

Fourier-transform conjecture. The function $F$ belongs to the Laguerre–Pólya class:

Let $G$ be a reductive Lie group, let $\mathfrak{g}$ be its Lie algebra, and let $\mathcal{O}\subset \mathfrak{g}^*$ be a nilpotent coadjoint orbit. Let $H\subset G$ be a Cartan su…