16 problems

Let $(\mathbb W,S)$ be a Coxeter system with a geometric $R$-realisation over a fusion ring $R$, and let $(\check{\mathbb W},\check{S})$ be the corresponding unfolded Coxeter syste…

Let $R$ be a fusion ring and let $(r_{s,t})_{s,t\in S}$ be a matrix satisfying the geometric conditions for a Coxeter system $(\mathbb W,S)$, as in the fusion-realisation condition…

Finiteness conjecture. There are only finitely many Woronowicz algebras having a given $(R^+,list)$ invariant.

Let $\mathcal{R}=\mathcal{R}_0$ be an integral fusion ring, and let $(\mathcal{R}_n)$ be the sequence obtained by iterating the integral extension construction of Proposition, star…

Let $P$ be the weight lattice, $P^+$ the dominant integral weights, $P_{\ell}\subset P^+$ the weights of level $ell$, and let $W_{ell}$ be the affine Weyl group with length functio…

Let $P$ be the weight lattice, $P^+$ the dominant integral weights, $P_{\ell}\subset P^+$ the weights of level $ell$, and let $W_{ell}$ be the affine Weyl group acting on the weigh…

Let $n\geq 2$ and let $k=-h^\vee+\frac{p}{2n-1}$ be an exceptional level. Let $\mathcal{K}(L_{p-h^\vee}(\mathfrak{so}_{2n+1}))$ be the Grothendieck ring of the corresponding affine…

Fusion-rule conjecture. There exists such a rational lisse vertex algebra whose irreducible modules satisfy

Let $k$ be an even positive integer, and let $\mathfrak{g}$ be a twisted affine Lie algebra not of type $A_{2\ell}^{(2)}$. Let $P_k^+$ be the set of dominant weights at level $k$,…

Let $(\widetilde N^{ab}_c,\widetilde s_a;N^{ij}_k,s_i;\mathcal N^{IJ}_K,\mathcal S_I;c)$ denote the specified fusion, spin, modular-extension and central-charge data, subject to th…

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

The singlet vertex algebra $\mathcal{W}(2,2p-1)$ is considered together with its module category, which is expected to be a braided tensor category, or at least to contain a suitab…

Let $\mathbb{G}$ be a compact quantum group, and suppose that its fusion semiring satisfies the freeness conjecture. Simplicity and unique trace conjecture. The reduced $C^*$-algeb…

Let $\mathbb{G}$ be a free unitary easy quantum group without any non-trivial one-dimensional representation. Let $\mathcal{C}^{\circ,\bullet}$ be its category of noncrossing color…

Let $\mathbb{G}$ be a free unitary easy quantum group. A free fusion semiring is obtained from a set $S$ with an involution and a binary law by taking the free monoid $R(S)$, with…

Let $I$ be the node set, let $t_a$ and $h^{\vee}$ be the parameters associated with the Dynkin diagram, and let $W^{(a)}_m$ be the elements of the WZW fusion ring defined from the…