7 problems

Let $\mathsf{X}_i^{(k)}$ denote the nonclassical divided-power web at position $i$ in $\mathbf{Web}(\mathfrak{so}_{2n+1})$, with $1\leq k\leq n$. Divided-power exchange relation co…

Let $(V,\mathbb{B}_V)$ be a based $U_{-q^2}$-module, for example a finite-dimensional irreducible type I representation with Lusztig canonical basis $\mathbb{B}_V$. Let…

Kirillov–Reshetikhin K-matrix conjecture. Symmetrizable invertible solutions of the generalized spectral reflection equation in tensor products of Kirillov–Reshetikhin modules, wit…

Meromorphicity conjecture. For all $V\in\mathcal{C}$, not necessarily irreducible, and for generic quantum symmetric pair parameters, $K_V(z)$ is the Laurent series expansion of a…

Affine factorization conjecture. In affine type, $\Upsilon$ admits an infinite-product factorization analogous to such a factorization of the quasi-$R$-matrix of quantum affine alg…

Parameter-inversion conjecture. There exists $g\in(U_q\mathfrak h)^{\mathcal W,\times}$ such that this relation is satisfied. Consequently, $k_{Y,\eta}$ specializes to a solution o…

Let $X \subseteq I$ be of finite type and let $\tau \in \operatorname{Aut}_X(A)$ satisfy $\tau^2=\operatorname{id}_I$ and $\tau|_X=\operatorname{id}_X$. For…