Isomorphism between the stable-envelope quantum algebra and the standard quantum affine algebra

Determine whether the quantum algebra U_q(ĥg_Q) constructed via K-theoretic stable envelopes for Nakajima quiver varieties is isomorphic to the standard quantum affine algebra U_q(ĥg_Q) associated with the same quiver Q. Establishing this isomorphism would, in particular, yield an explicit expression for the quantum difference operators M_L(z) in terms of the generators of U_q(ĥg_Q).

Background

The paper reviews the construction of quantum difference equations using the RTT formalism of K-theoretic stable envelopes, producing a ‘quantum algebra’ tailored to a Nakajima quiver variety. A central expectation in the field is that this algebra coincides with the usual quantum affine algebra for the corresponding quiver.

If this isomorphism holds, one obtains an explicit realization of the quantum difference operators M_L(z) directly in terms of the standard generators of U_q(ĥg_Q). The authors use this philosophy to connect representation-theoretic structures with the geometry of quiver varieties; they also note that for affine type A they address related constructions elsewhere, but the general isomorphism problem remains open.