5 problems

Let $\widetilde{\mathfrak{g}}$ be a twisted loop algebra with $\epsilon(\mathfrak{h})=0$. Let $\widehat{\rho}$ be the Weyl vector determined by the simple roots of…

Equality conjecture. The equality always holds:

Quantum-reduction irreducibility conjecture. The module $H(M)$ is irreducible; in particular, at most one homology group $H_j(M)$ is nonzero.

Let $N=n+m$, let $f$ be any nilpotent element of $\mathfrak{sl}_N$, and let … Here $s(\lambda)$ is the lattice-label map defined in the source, and $k$ and $\ell$ are related to…

Let $L(k\Lambda_0)$ be an admissible affine vertex algebra, and consider the (generalized) quantum Drinfeld–Sokolov reduction, which associates a $W$-algebra to suitable affine ver…