9 problems

Let $\mathfrak g$ be a simple Lie algebra over $\mathbb C$, let $u_q=u_q(\mathfrak g)$ be the corresponding small quantum group at a root of unity satisfying the stated assumptions…

The paper considers the affine Lie algebra $\hat{\mathfrak g}$, its central element $\mathbf k$, and truncated vertex operator algebras $\hat{\mathbf F}_{k+h^\vee}$ and…

Let $V$ and $W$ be simple vertex superalgebras of CFT type containing rank-one Heisenberg vertex algebras of opposite levels, with decompositions…

Fortuna's conjecture. The functor $\Psi_I$ is exact, and its degree-zero functor

Let $\mathbf{V}_{G_u,3}$ be the trinion vertex algebra with maximal untwisted punctures and let $\mathbf{V}_{1,1}$ be the mixed trinion vertex algebra. Let $i_1,i_2,i_3$ denote the…

Let $m,n$ and the levels $k,\ell$ be as in the source, and let $\pi^{k-\ell}$ be the rank-one Heisenberg vertex algebra. Semi-infinite-cohomology conjecture. The relative semi-infi…

Fix a positive level $\kappa$, set $q=\operatorname{exp}\left(\frac{\pi\sqrt{-1}}{\kappa'-\kappa_{\textup{crit}}}\right)$, and let $M$ be a $U^{\textup{Lus}}_q(\mathfrak{g})$-modul…

Let $J[0^N,(1)^{N'}]$ and $A[0^N,(1)^{N'}]$ be the finite arc algebras, let $\mathfrak{a}$ be the local-cohomology support ideal, and let $\mathsf{th}$ denote the homomorphisms ind…

Let $n$ be the dimension parameter specified in the source, and let $BV^i(N,N')$ denote the cohomology of the total Koszul bicomplex associated with the finite-dimensional approxim…