17 problems

Let an iterated $W$-algebra of type $A$ act on the equivariant homology space of an affine Laumon space, and let the shifted affine Yangian be the algebra constructed in the cited…

Let $\mathfrak{g}=\mathfrak{h}\oplus\mathfrak{u}(1)$, where $\mathfrak{h}$ is an ADE algebra or the super Lie algebra $\mathfrak{sl}_{n|m}$. The refined vacuum character of the aff…

Let the twisted affine Yangian be the extension of $TY_\hbar(\mathfrak{so}(2n))$ introduced in the paper, and let the affine Yangian associated with $\widehat{\mathfrak{sl}}(2n)$ b…

Let $TY_\hbar(\widehat{\mathfrak{so}}(2n))$ be the associative algebra generated by … with the defining relations specified in the paper. Let the affine Yangian associated with…

Let $K>2$, and let $Y^{K}$ be the $C[Chbar_1,Chbar_2]$-linear algebra obtained by gluing the two copies of the double deformed current algebra $A^K$ constructed from observables on…

Let a shifted affine super Yangian be a modification of the affine super Yangian adapted to the non-rectangular setting, and let a type $A$ $W$-superalgebra be the corresponding…

Let $A=U\big(\widehat{\mathfrak{gl}}(m_1+m_2|n_1+n_2)\big)$ and $B=U\big(\widehat{\mathfrak{gl}}(m_1|n_1)\big)$. Define the centralizer … Let … be the homomorphism from…

Let $N_1=q_1++q_w$ and $N_2=q_{w+1}++q_l$, and let $f$, $f_1$, and $f_2$ be the nilpotent elements defining the corresponding non-rectangular $W$-algebras. Let … be the affine Yang…

Affine Yangian centralizer decomposition conjecture. The centralizer $C(U(\widehat{\mathfrak{gl}}(m+n)),U(\widehat{\mathfrak{gl}}(n)))$ is isomorphic to the tensor product of the c…

Let the shifted affine Yangian associated with $\widehat{\mathfrak{sl}}(m)$ be defined using the anti-dominant weight $\beta$ and the generators $X^\pm_{i,r_i^\pm}$ and $H_{i,r_i}$…

The associative algebra $\mathsf Y^{(K)}$ is a new presentation of the affine Yangian of type $A_{K-1}$ for $K\neq 2$. Affine Yangian presentation conjecture. This presentation sho…

Let $\mathfrak{h}$ be an ADE algebra and set $\mathfrak{g}=\mathfrak{h}\oplus\mathfrak{u}(1)$. Consider the affine Yangian of $\mathfrak{g}$ and the universal enveloping algebra of…

Local-density exponential conjecture. Similar to the $\widehat{\mathfrak{gl}}(1)$ case, the operator $\mathcal{R}$ has the form

Let $M_i$ be representations of $\mathcal{W}^{\kappa_i}(\mathfrak{gl}_{N_i},f_i)$ for $i=1,2$, and let $\Phi_l$ be the map from the affine Yangian associated with the parabolic-ind…

Consider the last two toric configurations in Figure, namely the configurations associated with $\mathcal{O}(-1)\oplus\mathcal{O}(-1)\to\mathbf{P}^1$ and…

Let $\mathcal O(-p)$ be a line bundle over $\mathbb{C}\mathbf{P}^1$, and consider the analogue of the algebra associated with the relevant geometry. Shifted affine Yangian conjectu…

AGT limit conjecture. The limit of $\U^{(1)}_{q_1,q_2,q_3}$ as $q_1\rightarrow \omega_n$ and $q_2\rightarrow 1$ should be related to the affine Yangian of $\mathfrak{sl}_n$. This c…