6 problems

Let $\mathfrak{g}$ be a simple Lie algebra with simple roots $\alpha_i$, let $V_1,V_2$ be representations of $\mathfrak{g}$ with highest weights $\lambda_1,\lambda_2$, and let…

Rhin–Viola's conjecture. (i) If

Let a Lie algebra be given, together with its KZ differential equations and the associated dynamical difference equations. Consider hypergeometric integrals that satisfy the KZ equ…

Purity and exterior-power basis conjecture. For every $w\in Z_{r+1}$, the cohomology of $(\Omega^{\bullet}(Y),\nabla_{\tilde{\omega}})$ is pure,

Consider the quantum hierarchy associated with an affine Gaudin model with twist function. Its poles determine the integration contours, and affine opers provide the geometric data…

Mukhin–Varchenko conjecture. If the space $\operatorname{Sing}[\lambda+\mu-\sum_{i=1}^n k_i\alpha_i]$ of singular vectors is one-dimensional, then