9 problems

Let $p_+$ and $p_-$ be the parameters of the logarithmic $(p_+,p_-)$ model. Let ${\bar{\mathscr{C}}}$ be the space of generalized characters, let $\mathscr{G}$ be the subspace desc…

Kazhdan–Lusztig correspondence conjecture. The category of $\mathcal{W}(p)$-representations is equivalent to the category of finite-dimensional…

Let $\mathfrak{g}$ be a semisimple finite-dimensional complex Lie algebra with simple roots $\alpha_1,\ldots,\alpha_n$ and Killing form $(-,-)$. For an integer $p\geq 2$ divisible…

Projective-character submodule conjecture. The subspace $\mathcal{P}$ is an $\mathcal{L}_{1,0}^{\mathrm{inv}}(\bar U_q)$-submodule of $\operatorname{SLF}(\bar U_q)$. The subspace i…

Jordan-cell rank conjecture. In the scaling limit of $\mathcal{T}_{0,\mathfrak{q}^2}$, states from limits of irreducible $\mathcal{X}_{j,P}$ subquotients should be involved in Jord…

For $p\geq 3$, let ${\mathcal V}^{(p)}$ be the generalized vertex algebra introduced by … Consider its modules in the category $\mathcal{O}$. Module-category conjecture. For every…

Fix $s$ with $1\,{\leqslant}\, s\,{\leqslant}\, p-1$. Let $\mathrm{Ext}^\bullet_s$ be the associative Yoneda algebra formed from the extension spaces between the specified irreduci…

Let $p,p'\in\mathbb{Z}_{>0}$ with $p\ne p'$ and $p\geq 2$. Let $L=\mathbb{Z}\alpha$ satisfy $\langle\alpha,\alpha\rangle=2pp'$, and let $\mathcal{W}(p,p')$ be the vertex operator a…

Let $p\geq 2$, let $W(p)$ be the triplet vertex operator algebra, and let $\overline{U}_q(\mathfrak{sl}_2)$ be the restricted quantum enveloping algebra associated to…