3 problems

Cuspidal short exact sequence conjecture. For non-symmetric $\mathsf{C}$, let $\rho\in\Phi_+^{\mathrm{re}}$, and let $(\beta,\gamma)$ be a real minimal pair for $\rho$. Then there…

James conjecture. Let $\alpha\in Q_+$, and let $L_K$ be an irreducible $R_\alpha(K)$-module which factors through $R_\alpha^{\boldsymbol{\Lambda}}(K)$. Then reduction modulo $p$ of…

Let $(I,\cdot)$ be a Cartan datum of finite type, let $Q_+$ be its positive root lattice, let $\alpha\in Q_+$, and let $R_\alpha$ be the corresponding Khovanov–Lauda–Rouquier algeb…