Monodromy quantum group isomorphism conjecture

Let QQ be a quiver, let UqMO(g^Q)U_{q}^{MO}(\hat{\mathfrak{g}}_{Q}) be the MO geometric quantum affine algebra, let Uq(g^Q)U_{q}(\hat{\mathfrak{g}}_{Q}) be the corresponding quantum affine algebra, and let Uq(gm)U_{q}(\mathfrak{g}_{\mathbf{m}}) and Bm\mathcal{B}_{\mathbf{m}} be the root subalgebra and its corresponding algebra associated with a parameter m\mathbf{m}.

Monodromy quantum group isomorphism conjecture. There are isomorphisms of algebras

UqMO(g^Q)Uq(g^Q),Uq(gm)Bm.U_{q}^{MO}(\hat{\mathfrak{g}}_{Q})\cong U_{q}(\hat{\mathfrak{g}}_{Q}),\qquad U_{q}(\mathfrak{g}_{\mathbf{m}})\cong\mathcal{B}_{\mathbf{m}}.

These isomorphisms are used to relate the MO quantum affine algebra and its root subalgebras to the algebras arising in the construction of the quantum difference equation. The source does not state whether this conjecture has been resolved.

Sources & referencesView supporting material

Primary source

Tianqing Zhu, “Quantum difference equation for the affine type A quiver varieties I: General Construction”, arXiv:2308.00550 (2024).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.