6 problems

Let $\triangle(n)$ be the cyclic quiver, let $\mathcal Z=\mathbb Z[\upsilon,\upsilon^{-1}]$, and let $\boldsymbol{\mathfrak D_{\!\vartriangle\!}}(n)$ be its double Ringel–Hall alge…

Prime-degree denseness conjecture. There exists a positive integer $m$ (in terms of $q$) such that for any form

For a dominant coweight $\unl{\lambda}$ and a coweight $\mu$, let $\fU^{\ad,\mu}_\vv[\sz^{\pm1}_1,\ldots,\sz^{\pm1}_N]$ be the integral form of the shifted quantum affine algebra,…

Let $\Lambda$ be the Leech lattice, let $V_\Lambda$ be its lattice vertex operator algebra, and let $V^\natural_\mathbb{Z}$ be the integral form of the Moonshine module. For…

Assume $(C,\mathbf i)$ is of type (i), and let $\kappa$ be the algebra isomorphism from the associated quantum cluster algebra $\mathcal A^\dagger(\mathbf i)$ to the quantum unipot…

Let ${\mathcal Z}$ denote the integral coefficient ring, let ${{\mathfrak H}_{\!\vartriangle\!}(n)_{{\mathcal Z}}}$ be the integral Ringel–Hall algebra associated with the cyclic q…