5 problems

Monodromy generation conjecture. The monodromy representation is generated by the operator $\mathbf{B}_{\mathbf{m}}$.

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

Let $\mathfrak{h}^{\mathrm{reg}}$ be the regular locus for the Cartan subalgebra and let the boundary Casimir connection descend to the quotient $\mathfrak{h}^{\mathrm{reg}}/W$, wh…

Elliptic Casimir monodromy conjecture. By analogy with the rational and trigonometric cases, the monodromy of the elliptic Casimir connection is described by the quantum Weyl group…

Monodromy conjecture. The monodromy of the trigonometric Casimir connection is equivalent to the quantum Weyl group action of the affine braid group $\widehat{B}$ on finite-dimensi…