18 problems

Let $U_{q,p}(\widehat{\mathfrak{sl}_2})$ be the elliptic algebra introduced in the paper, with screening currents and representation spaces as constructed there. The q-deformed ext…

Universal-twist evaluation conjecture. The TLA represented by a double arrow in the figures is conjectured to be the evaluation of a universal twist.

Let $Q_{2m}(\mathcal E)$ be the elliptic algebra containing the constructed commuting elements $f(u)$, and let $q_{2m}(\mathcal E)$ be its classical counterpart. The Lenard scheme…

Let U_{q,p}(chat{\bf sl}}_N) be the elliptic algebra in which the half currents and the $L$-operator $chat{L}^+(v)$ are defined, with spectral variables $z_i=q^{2u_i}$ for…

Let $n$ and $k$ be coprime positive integers with $1\le k<n$, let $d\in\mathbb N$, and let $R_{n,k}(\mathcal E,\eta)$ be the corresponding elliptic solution of the Yang–Baxter equa…

Let $\mathcal E$ be an elliptic curve, let $\eta\in\mathcal E$, and let $n$ and $k$ be coprime positive integers with $1\le k<n$. Define $Q_{n,k}(\mathcal E,\eta)$ by generators…

Elliptic vertex-operator commutation conjecture. These vertex operators satisfy the commutation relation given by the source equations with the elliptic $R$-matrix, the choices…

The elliptic-algebra module and vertex-operator conjecture. The elliptic algebra ${\cal A}_{q,p}(\widehat{sl_2})$ has natural analogs of the level-one modules ${\cal H}^{(i)}$,…

Let ${\cal A}_{q,p}(\widehat{sl}_2)$ denote the elliptic algebra associated with the quantum affine algebra $\widehat{sl}_2$, with parameters $q$ and $p$. The elliptic-algebra symm…

Consider elliptic quiver BPS algebras and a higgsing operation relating a parent theory to a higgsed theory. The source expects the induced map, when it exists, to preserve the cen…

Let $B_{V,\Psi}$ be an untwisted elliptic algebra, and let its center be denoted by $Z(B_{V,\Psi})$. A filtered deformation induces a trivial deformation of the center when the cor…

Let $B_{V,\Psi}$ be an elliptic algebra, and let a filtered deformation mean a nontrivial filtered deformation of $B_{V,\Psi}$. Let $A^+_M$ denote the Rees algebra associated with…

Let $Q_{n,k}(E,\tau)$ be a Feigin–Odesskii elliptic algebra, where $E$ is an elliptic curve and $\tau\in E$. For generic $\tau$, its homogeneous components have the same dimensions…

Let $T$ and $T'$ be elliptic algebras with equal graded quotient rings … A blowup or blowdown is the corresponding birational operation on elliptic algebras described in the paper.…

Let $R$ be an elliptic algebra, and let a line module mean a line module in the sense of the paper. A minimal model is a minimal elliptic surface obtained from $R$ by the relevant…

Exceptional-line projective-dimension conjecture. Then

Let $U_{q,p}(B_l^{(1)})$ be the elliptic algebra with level-$1$ currents $e_j(z)$ and $f_j(z)$, and let ${\cal F}_{\lambda,\xi,\kappa}(\Lambda+\mu,\mu)$ denote the modules appearin…

Let $U_{q,p}(\widehat{\mathfrak g})$ be the elliptic algebra associated with a general untwisted affine Lie algebra $\widehat{\mathfrak g}$, and consider the coset…