10 problems

Let $X$ be an adjoint variety of type $A_n$, and let $Y\subset X$ be a general hyperplane section. Let ${\rm QH}(X)_{\rm can}$ and ${\rm QH}(Y)_{\rm can}$ denote the restrictions o…

Let $R_{\sigma\tau}^{(n)}(t,\lambda)$ be the coefficient of $\hbar^n$ in the asymptotic solution matrix $R_{\sigma\tau}(t,\lambda,\hbar)$ of the equivariant quantum differential eq…

Let $G$ be the group in the paper, let ${\mathcal I}_G$ be the indicated category of $G$-modules, and let $N$ denote the filtration used to define $gr^N_jW$. Semisimplicity conject…

Assume $p\nmid(e+1)$, let $I=\\{0,1,\ldots,e\\}$, and let $R^{\Lambda}_n(I)$ denote the cyclotomic quiver Hecke algebra associated with a dominant integral weight $\Lambda\in P^+$.…

Let $X$ be an adjoint or quasi-minuscule variety as above, and let $Y\subset X$ be a general linear section. Write ${\rm BQH}(Y)$ and ${\rm QH}(Y)$ for its small and big quantum co…

Let $X$ be a smooth projective variety of dimension $n$ over $\mathbf{K}$, and let $f$ be a polarized self-morphism as in the generalized Weil's Riemann hypothesis:…

Let $\mathfrak{g}$ be a semisimple Lie algebra. Semisimplicity conjecture. The category of finite-dimensional $D(U_q(\mathfrak{g}))$-modules is semisimple. The source attributes th…

Let $\mathfrak{g}$ be a semisimple Lie algebra, and let $U_q(\mathfrak{g})$ be its quantized enveloping algebra with quantum double $D(U_q(\mathfrak{g}))$. A finite-dimensional rep…

Let $V^{\bullet}$ be the sheaf constructed in the paper from closed differential forms and related quotients. Semisimplicity conjecture. The sheaf $V^{\bullet}$ is semisimple. The…

Semisimplicity conjecture. (i) If $n=2k+1$, then $B_n(\hat{z})$ is semisimple only if $\kappa\mathfrak{S}_n$ is semisimple and $p_{2k-1}(\hat{z})\ne 0$. (ii) If $n=2k$, then…