9 problems

Let $W^{(j)}(z)$ be the currents of the deformed $W_n$ algebra (DWA), and let ${\overline X}_{\alpha}(\lambda)$ denote the screening operators defined by (SET1). An intertwiner is…

Elliptic quantum group formulation conjecture. The elliptic quantum groups $U_{q,p}(\widehat{\mathfrak g})$ and $U_{t_1,t_2,p}(\mathfrak{gl}_{tor})$ give alternative formulations o…

Conjecture 1. The same mutual commutativity relation as in the $A_l^{(1)}$ and $D_l^{(1)}$ cases holds for ${\mathfrak g}=E_l^{(1)}$:

Let $X$ be a two-sided Hecke pattern of rank $r$. Write $H_*(X)$ for its Borel–Moore homology, and let $W_{\star,\star}(S)$ denote the algebra with the appropriate choices of indic…

Let $G$ be a non-simply laced Lie group with lacing number $r^\vee$, let $\mathcal W_{q,t}(\mathfrak{g})$ be the associated deformed $W$-algebra, and let…

Identification conjecture. The $q$-deformed $\mathcal{W}_{1+\infty}$ algebra should be the same as the $\mathcal{W}_{\infty}[\mu]$ algebra used in higher-spin…

Let ${\bf g}$ be an untwisted affine Lie algebra or the twisted affine Lie algebra of type $A^{(2)}_2$, and let $U_{q,p}({\bf g})$ be the associated elliptic algebra with elliptic…

Let ${\cal I}_n$, for $n=1,2,\ldots$, be the Local Integrals of Motion, and let ${\cal G}_m$, for $m=1,2,\ldots$, be the Nonlocal Integrals of Motion, for the deformed $W$-algebra…

Let ${\cal I}_n$, for $n=1,2,\ldots$, be the Local Integrals of Motion for the deformed $W$-algebra $W_{q,t}(\widehat{sl_N})$, defined by analytic continuation when necessary. Let…