35 problems

Let $\mathcal{W}_p$ be the triplet VOA and let $\overline{U}_q(\mathfrak{sl}_2)$ be the restricted quantum group at a $2p$-th root of unity. FGST equivalence conjecture. The repres…

For each integer $p\,{\geqslant}\, 2$, let $\mathfrak{C}_p$ be the category of representations of the triplet $\boldsymbol{\mathcal{W}}(p)$ algebra whose adjoint $L_0$-eigenspaces…

Creutzig–Milas conjecture. This Verlinde algebra is isomorphic, as a ring, to the Grothendieck ring of the singlet algebra.

Let $\sigma^{\ell}$ denote spectral flow by $\ell$, and let $\mathcal{M}$ and $\mathcal{N}$ be $\mathfrak{G}$-modules with fusion product $\mathbin{\times}$. Spectral-flow compatib…

Consider the logarithmic conformal field theory obtained from the quantum-group-symmetric CFT in the limit $\mu\to 3$, together with its unitary Ising subsector. Ising subsector lo…

Let $V$ be one of the vertex algebras specified by the paper's extension pairs, let $A$ be the corresponding free field algebra, and let $\mathfrak{N}$ be the Nichols algebra gener…

Let $\mathcal{V}_{\mathcal{SF}_n^{\mathrm{even}}}$ be the even part of the vertex superalgebra of $n$ pairs of symplectic fermions, and let $\mathcal{C}_0\oplus\mathcal{C}_1$ be th…

Let $\mathcal{V}_{\Lambda^\oplus}$ be the lattice vertex operator algebra and define … The short-screening construction is conjectured to have the following properties. Screening-c…

Let $\mathcal{W}^{log}$ be the proposed logarithmic conformal field theory, and let the smaller long-screening kernel be the corresponding subalgebra. Kazhdan–Lusztig correspondenc…

Let $\mathrm{W}$ be the kernel intersection of the short and long screenings inside $\mathcal{V}_{\Lambda^{long}}$, and let $\mathcal{W}^{log}$ be the larger subspace obtained by i…

Let $p'$ be the minimal-model parameter, and let $\langle\mathcal{K}_{1,3}\rangle$ be the unital fusion subring generated by $\mathcal{K}_{1,3}$. Let $U_n$ and $T_n$ denote the Che…

Let $p$ be the minimal-model parameter, and let $\langle\mathcal{K}_{3,1}\rangle$ denote the fusion subring generated by $\mathcal{K}_{3,1}$. Write $\mathcal{S}_{kp,1}^{a,0}$ for t…

Let $p$ be the minimal-model parameter and let $\mathcal{K}_{3,1}^{\mathbin{\times} n}$ denote the $n$-fold iterated fusion product of $\mathcal{K}_{3,1}$. Iterated-fusion decompos…

Let $p$ and $p'$ be the minimal-model parameters, and consider the Kac modules $\mathcal{K}_{r,s}$ appearing in the decompositions of…

Let a consistent boundary conformal field theory have modules defining its boundary sectors. Fusing with a Neveu–Schwarz module is considered as a functor on the chosen category of…

Let $\mathscr{C}$ be the abelian category of ghost vertex operator algebra modules generated by imposing closure under extensions from the typical modules…

Grothendieck–Verlinde fusion ring isomorphism conjecture. The product on the resulting Grothendieck ring may be identified with the Verlinde product under the group isomorphism…

Let $F=F_{C}$ be the bulk state space of a full conformal field theory, and let ${\mathrm{Cor}}_{g;n}$ denote its correlation functions for orientable world sheets of genus $g$ wit…

Charge-conjugation bulk-state decomposition conjecture. As a left module over a single copy of the chiral algebra ${\mathscr V}$, the bulk state space decomposes as

Let $\mathscr{W}\equiv\textup{\textsf{\textbf{W}}}(2,(2p)^{\times 3\times 2})$ and let $\textup{\textsf{\textbf{Z}}}_{s,r;\vartheta}^{\alpha,\beta}$ be the modules considered in th…

Let $p$ be the parameter of the algebra $\mathscr{W}\equiv\textup{\textsf{\textbf{W}}}(2,(2p)^{\times 3\times 2})$, and let…

Let $\mathcal{W}'_{\mathfrak{q},N}$ be the associative algebra in the XXZ representation generated by $W\!B^{\alpha}_j$, with $1\leq j\leq N-2p+2$ and $\alpha\in\{0,\pm\}$, togethe…

Let $\mathcal{S}$ be the interchiral algebra, and consider the direct summands in the decomposition of the relevant state space for each finite $j$. Equip these direct summands wit…

Let $\mathfrak{S}$ be the Lie algebra generated by modes of bilinears in fermionic fields, and let $\mathfrak{S}_{\infty}$ be the Lie algebra generated by bilinears in fermion mode…

Let $\epsilon$ be the parameter governing the limiting procedure to the logarithmic theory, and let the different definitions of the field $\psi_2(z)$ arise from the alternative fu…