19 problems

Universal formula conjecture. The formula

Let $M,N_1,N_2\in\mathbb{Z}$. The algebras $\mathcal{A}_{M,N}$ contain a subalgebra $\mathcal{K}_{M,N}$ extending the commuting quantum toroidal $\mathfrak{gl}_1$ algebras, and…

Quantum toroidal superalgebra isomorphism. There is an isomorphism

D6 $qq$-character BPS-crystal conjecture. For $i\in Q_0$, the $qq$-characters are

Gauge-origami Bethe ansatz conjecture. The Bethe ansatz equations are

Hopf algebra isomorphism conjecture. The map $\Upsilon$ induces a Hopf algebra isomorphism

R-matrix correspondence conjecture. The endomorphism

Let $\mathcal{F}_{\Lambda}$ be the Fock representation with screening operators $\xi_i$ and $\eta_i$ for $i\in\hat{I}^-\cup\{m\}$, and set … For a weight $\Lambda$, let…

Let $U_q\,\widehat{\mathfrak{sl}}_{m|n}$ be the quantum affine algebra and let ${\mathcal E}_{m|n}$ be the quantum toroidal algebra. Define…

Let $\mathcal E_{q^{-4},q^2,q^2}$ be the specialized elliptic Hall algebra, let $\widehat{\mathcal E_{q^{-4},q^2,q^2}}$ denote its completion, and let…

Let $\mathcal E_{q_1,q_2,q_3}$ be the elliptic Hall algebra with $q_1q_2q_3=1$, and let $\mathcal E_{q^{-4},q^2,q^2}$ be its specialization at $(q^{-4},q^2,q^2)$. Let…

Quantum toroidal $\mathcal E_2$ Bethe ansatz conjecture. For each such eigenvector, there exist polynomials $Q_0$ and $Q_1$ whose roots satisfy the two displayed Bethe ansatz equat…

Let $\mathcal{O}^{fin}_{{\mathcal B}^\perp}$ be the category of finite-type modules, let $R=\operatorname{Rep}\,\mathcal{O}^{fin}_{{\mathcal B}^\perp}$ be its Grothendieck ring, an…

Let $\mathcal{O}^{fin}_{{\mathcal B}^\perp}$ be the category of finite-type modules, and let $K_0(\mathcal{O}^{fin}_{{\mathcal B}^\perp})$ denote its completed Grothendieck ring. F…

Fix non-negative integers $l_1,\dots,l_t,l'_1,\dots,l'_t$, and for sufficiently large $k$ let $L_k=(l_1,\dots,l_t,0,\dots,0,l'_t,\dots,l'_1)$ be the vector with $k$ components. Let…

Let $\mathcal E_n$ denote the quantum toroidal algebra, and let…

Let $\widehat{\widehat{\mathfrak{g}}}$ be the double-affine algebra in the sense of the paper, and let $B_{\widehat{\widehat{\mathfrak{g}}}}$ be its double affine braid group. A do…

Let $\widehat{\widehat{\mathfrak{g}}}$ denote the double-affine extension associated to the affine Kac–Moody algebra $\widehat{\mathfrak{g}}$. Consider the 2-representations of…

Let $\widehat{\mathfrak{g}}$ be the affine Kac–Moody algebra and let the geometric categorical $\widehat{\mathfrak{g}}$ action on…