4 problems

Braverman's conjecture. The partition function $Z(m)$ must be very closely related to the eigenfunction $Y(m)$. The conjecture proposes a relation between generating functions of i…

Let $N$ be a positive integer, let $x_i$, $b_i$, $d_i$, and $\overline{d}_i$ be parameters, and let $\mathcal{H}^{{\widehat{\mathfrak{gl}}_N}}(x_i;b_i,d_i,\overline{d}_i,q,\kappa)$…

Let $\mathcal{H}^{e\text{RS}}_k$ be the elliptic Ruijsenaars-Schneider Hamiltonians for $k=1,\dots,N-1$, and let $\mathcal{Z}^{\text{RS}}(\textbf{a},\textbf{x})$ be a function of t…

Let $N-1$ degrees of freedom of the quantum double elliptic (DELL) system be described by the current $\mathcal{O}(z)$ and let $\mathcal{Z}^{DELL}_{\text{inst}}(p,x_1,\dots, x_N)$…