6 problems

Degeneration conjecture. As $\kappa\rightarrow0$, the quantum difference equation degenerates to the trigonometric Casimir connection.

Let $\mathcal{L}_i$ be the line bundle in the affine type $A_{r-1}$ Hilbert-scheme example, let $\mathbf{M}_{\mathcal{L}_i}(z)$ be its quantum difference operator, and let $H$ be a…

Let $M(\mathbf{v},\mathbf{w})$ be an affine type $A$ quiver variety, and let $\mathbf{M}_{\mathcal{L}}(z)$ denote its quantum difference operator for a line bundle $\mathcal{L}$. L…

Monodromy quantum group isomorphism conjecture. There are isomorphisms of algebras

Okounkov's shift-operator conjecture. In the stable basis, the operator $S_\mathsf{w}$ is conjugate to

Okounkov's wall-operator conjecture. The wall operator is given by