14 problems

For supersymmetric quantum mechanics with a generic quiver $\mathfrak{Q}$ as target space, let $Y(\mathfrak{Q})$ denote the respective quiver Yangian algebra. Quiver Yangian conjec…

Spherical shuffle realization conjecture. The homomorphism $\xi$ can be promoted to an algebra isomorphism

Let $\mathrm{Q}$ be a quiver defining a three-dimensional $\mathcal{N}=4$ quiver gauge theory with unitary gauge group, and let $(\widehat{Q},\widehat{W})$ denote the triple quiver…

BPS states in supersymmetric theories may carry algebraic structures, such as quiver Yangian structures, whose representations depend on stability parameters and their chambers. Wa…

Let twisted quiver Yangians be constructed as associative subalgebras of quiver Yangians, and let their truncations be the algebras obtained by imposing the corresponding level con…

A twisted quiver Yangian is a subalgebra of a quiver Yangian, and let $\widetilde{\mathcal{Y}}\left(\widehat{\mathfrak{l}}\right)$ denote the twisted quiver Yangian associated with…

Let $Q_K$ be a quiver arising from the knot-quiver correspondence, and let the underlying three-dimensional $\mathcal{N}=2$ theory be the theory associated with that correspondence…

Let $(Q,W)$ be a quiver with potential, and let $J_{(Q,W)}$ be its Jacobian algebra. A finite-codimensional ideal is an ideal of finite codimension in this algebra. Ideal-counting…

Let $|\mu'\rangle=e^{(a)}_0|\mu\rangle$, where $|\mu\rangle$ is a state generated only from operators $e^{(a_i)}_0$. Let $\mathcal{T}_{\varnothing,\mu}(u)$ be given by … Here…

Let $\mathcal{T}_{\mu_1,\mu_2}$ denote matrix elements of the operator $\mathcal{T}$ between states labelled by partitions or related quiver data. In the known cases, for…

Let $\mathtt{Y}$ be a quiver Yangian, with positive part $\mathtt{Y}^+$ and dual $\mathtt{Y}^{+*}=\hom_\mathbb{C}(\mathtt{Y}^+,\mathbb{C})$. The Drinfeld double conjecture. The Dri…

Quiver Yangian–BPS equivalence conjecture. With this prescription, the equivalence between the quiver Yangian and BPS algebra descriptions should extend to all representations, inc…

Let $X$ be a Calabi–Yau manifold admitting multiple dual quiver gauge theories $(Q,W)$ related by Seiberg dualities, also called quiver mutations. For each such pair, let…

For a toric Calabi–Yau threefold, let $\mathsf{Y}_{(Q,W)}$ denote the quiver Yangian associated with its quiver $Q$ and superpotential $W$, and let $\operatorname{CoHA}$ denote the…