9 problems

Let $\widehat{\mathfrak g}^{\rm tw}$ be the twisted affine algebra, let $\mathcal O$ be its category of modules, and let $H_j$ denote the homology of the twisted quantum Hamiltonia…

Let $\lambda=(\lambda_1\leq\lambda_2\leq\dots\leq\lambda_n)\vdash N$, and set $\widehat{\lambda}_i=(1,\dots,1,\lambda_i)\vdash N_i$ with $N_i=N-\sum_{j>i}\lambda_j$. Write…

Braided tensor equivalence conjecture. The functor $H_f^0$ is an equivalence of braided tensor categories. The source already states that this functor is an equivalence of abelian…

Spectral-flow conjecture. For every $\lambda\in\mathrm{Pr}_{\mathbb{Z}}^k$ and $0\leq\theta\leq\bar q$, there exists $\mu\in\mathfrak{h}^*$ such that

Let ${\mathfrak g}$ be a simple Lie algebra, let $({\mathfrak a}_1,\ldots,{\mathfrak a}_L)$ be ordered subalgebras whose direct sum is a subalgebra of ${\mathfrak g}$, and let…

Let $n,m$ be positive integers and let $p$ satisfy … Let $\mathcal{W}_{n,m}$ be the family of W-algebras defined by quantum Hamiltonian reduction, let…

Reduced W-algebra identification conjecture. The reduced algebra is isomorphic to the W-algebra $U(\mathfrak{g},e_2)$:

Let $\mathfrak{g}$ be a semisimple Lie algebra of type $A$, and let $e$ and $e'$ be nilpotent elements such that $e'$ covers $e$ in the dominance ordering. Let…

Let $n>1$, and let $\varphi_n:\mathfrak{sl}(2)\rightarrow\mathfrak{sl}(n)$ be an embedding such that, as $\mathfrak{sl}(2)$-modules, $\mathfrak{sl}(n)$ decomposes as … where…