4 problems

Let $n=3$, let $\Lambda\in P_{+}^{(2,4)}$, and write $\zeta=m(\eta)\in\mathbb{Z}_{+}^{2}$. Three-colour configuration-sum conjecture. … The source calls this a conjecture and uses…

Let $k\geq1$, $a\in\{0,1\}$, and let $\eta$ be a partition with multiplicity vector $m(\eta)$. Level-rank configuration-sum conjecture. For the parameters appearing in the source,…

Let $\hat{\mathfrak{g}}=X_n^{(1)}$ be as in the classically restricted setting, let $B=\bigotimes_{a=1}^n\bigotimes_{i\ge1}(B^{a,i})^{\otimes L_i^{(a)}}$, and let…

Let $\hat{\mathfrak{g}}=X_n^{(1)}$, with $X=A,B,C,D$ or $E$ for $n=6,7,8$, $F$ for $n=4$, or $G$ for $n=2$. Let … where $L_i^{(a)}\in\mathbb{N}$ and only finitely many are nonzero.…