6 problems

Let $\beta\in\mathbb C$ and $n\in\mathbb N$. Let $d_n^{(\beta)}$ denote the dimension or counting quantity defined in the source for the degree-$n$ states at momentum $\beta$, and…

For each $k\geq 1$, let $\Sigma_{k,m}$, for $m\geq 1$, be the weight-$k$ spectral curve … Here $\mathscr{P}_k$ denotes the set of partitions of weight $k$, and $\ell(\lambda)$ deno…

Weak BLZ conjecture. For every $\alpha$ and $L$, the number of solutions of the BLZ system is at most $p(N)N!$. For generic values of $\alpha$ and $L$, the number of solutions is…

Let $P_n(N)$ be the number of $n$-coloured partitions of $N$, let $n=\operatorname{rank}\mathfrak{g}$, and let $\operatorname{systemonc}$ denote the displayed system of equations f…

Let a quantum $\widehat{\mathfrak{g}}$-KdV oper be an oper of the form … with the additional regular singularities chosen to have trivial monodromy for every value of $\lambda$. Le…

Affine Gaudin Bethe ansatz conjecture. Every eigenvalue of $\boldsymbol G_n$ in the level-$N$ subspace has the form $r_n(\bar s,\bar t)$ for a solution of the affine Gaudin Bethe a…