15 problems

The PBW filtration conjecture. One has

Fusion-product independence conjecture. The corresponding fusion product does not depend on $Z$ as a representation of $\g\otimes\mathbb{C}[u]$.

Let $\widehat{\mathfrak{g}}$ be an affine Kac–Moody algebra, let $\Lambda=m\Lambda_0+\lambda$ be a dominant integral weight, and let $V(\Lambda)$ and $V(\lambda)$ denote the corres…

Affine vertex algebra–small quantum group correspondence conjecture. The category … associated with $$ .

Let $\mathfrak{g}$ be an untwisted affine Kac–Moody Lie algebra, let $\rho$ be the affine Weyl weight used in the tensor product $V(\rho)\otimes V(\rho)$, and let…

Let $\mathfrak{g}$ be an untwisted affine Kac–Moody Lie algebra, let $\delta$ be its null root, and let $\lambda\in\mathcal{P}^+$ be a dominant integral weight of positive level. F…

Let $\mathfrak{g}$ be an affine Kac–Moody algebra, let $V$ be a weight module, and let $\mathfrak{C}$ be the set of normal quasicones arising as annihilators of vectors in $V$. Let…

Fix $e,\ell,m>0$ and let $\nu\in\mathbb{N}^{\ell}(m)$. Let $\mathcal{O}^{\nu}(n)$ be the affine category block decomposition introduced in the source, let $\mathbf{S}^{\nu}(n)$ be…

Let $e,\ell,m>0$, let $\nu\in\mathbb{Z}^{\ell}(m)$, and let $\mathcal{O}^{\nu}_{\mu,a}$ denote the block defined by … with $a\in\mathbb{N}$. Chuang–Miyachi's conjecture. The blocks…

KNO conjecture. For any $i\in I\setminus\{0\}$, there exists a unique variety $X$ endowed with a positive $\mathfrak g$-geometric crystal structure and a rational map…

Let $G$ and $\mathfrak g=\langle \mathfrak t,e_i,f_i\rangle_{i\in I}$ be the affine Kac–Moody group and algebra associated with a generalized Cartan matrix, and let $B^-_w$ be the…

Let $MOp$ be the scheme of Miura opers with nilpotent singularities, and let $bD^b(hgcritoperatorname{mod}nilp)^{I^0}$ be the Iwahori-monodromic derived category of critical-level…

Let $\Gamma_\Fl:\bD_{\mathrm{ren}}(\fD(\Fl^{\operatorname{aff}}_G)_\crit\operatorname{mod})\to\bD_{\mathrm{ren}}(\hg_\crit\operatorname{mod}_\nilp)$ be the global-sections functor,…

Let $Op$ be the space of opers with nilpotent singularity, let $tN/cG$ be the nilpotent-cone quotient, and let … be the ind-completed categorical base change. Let … be the extende…

Frenkel–Gaitsgory conjecture. The category $\KLlam$ is semisimple for every $\slam\in \bar P^+$, and, for each $\lambda\in \Paf{\operatorname{crit}}$, there is an isomorphism