10 problems

Let $\boldsymbol{\boldsymbol{\text?}}$ be a tensor product parameter with associated free abelian group $S^{\boldsymbol{\boldsymbol{\text?}}}(V_{\mathbb Z})$, and let…

Let $(i,a)\in I\times_2\mathbb Z$ and $w\in W$, and let $Q_{w\varpi_i,a}$ be the corresponding formal solution of the extended $QQ$-system. Let $\chi_{\ell}$ denote the $\ell$-char…

Let $(i,a)\in I\times_2\mathbb Z$, let $w\in W$, and let $Q_{w\varpi_i^{\vee},a}$ be the corresponding $Q$-variable. Let $\chi_{\ell}$ denote the $\ell$-character and let…

Let $\mathcal{O}_{sh}^{\mathbb Z}$ be the integral finite-length subcategory of shifted category $\mathcal{O}_{sh}$, and let $\mathscr A$ be the cluster algebra associated with the…

Let $V_1,V_2,V_3$ be objects of the shifted category $\mathcal{O}_{sh}$. Associativity conjecture. There exists an isomorphism … Thus, $k$-fold tensor products in…

Let $\mathfrak{r}$ be the group equipped with the involution $d$. The group-automorphism conjecture. The involution $d$ of $\mathfrak{r}$ is a group automorphism. This is proposed…

Let $\tau$ be the diagram involution, let $\bar{\mathbf{v}}_j$ denote the associated class of the dimension vector at $j$, and let $\bm z$ be the central parameters. For a dominant…

Let $\mathfrak{g}$ be the Lie algebra under consideration, let $\mu$ be the corresponding shift, and let $Y^{\mu}(\mathfrak{g})$ be the associative algebra defined by the RLL relat…

Let $\lambda$ be a dominant coweight and let $\mu\leq\lambda$ be a coweight such that $\mu+\alpha_i^\vee\leq\lambda$. Let $Y_\mu^\lambda(\mathbf{R})$ be the truncated shifted Yangi…

Let $\rho$ be a cocharacter of $SL_N$, and use the combined $\mathbb C^\times$-action on $U^{comb}_\delta(\mathscr O_\epsilon(\mathbb C^2)\otimes\mathfrak{gl}_N)$ obtained from the…