7 problems

Three-legs PT3 $qq$-character collision conjecture.

Let $\mathsf{T}_{\four}^{K}(x)$ denote the D8 $qq$-character and let $\mathsf{f}^{K_{1}|K_{2}}_{\four\four}(x_{1}/x_{2})$ be the corresponding one-loop factor. D8 quadratic commuta…

D6 $qq$-character BPS-crystal conjecture. For $i\in Q_0$, the $qq$-characters are

Let $\Gamma$ be a finite-type quiver and fix $i\in\Gamma_0$. Consider a weight dimension vector with a single nonzero entry, $w_i\neq 0$ and $w_j=0$ for $j\neq i$, and let…

Let $\Gamma$ be a generic quiver and let $w=(w_i)_{i\in\Gamma_0}\in\mathbb{Z}_{\ge 0}^{\operatorname{rk}\Gamma}$ be a generic weight dimension vector. Let…

Let $c7$ be an admissible $qq$-character with a dominant monomial. Its graph may be equipped with a supplement satisfying the compatibility condition around every square, and an in…

Let $c7_1,c7_2$ be simple $qq$-characters, and define their combinatorial fusion $c7_1*c7_2$ by retaining the products of monomials with maximal relative pairing. Suppose this fusi…