Neguț's stable-basis realization conjecture for the quantum affine quiver algebra

About 5 years old · traced to

Let A\mathcal A be the algebra defined by the action-product map from the shuffle-algebra construction, and let Uq(g^Q)U_q(\widehat{\mathfrak g}^Q) be the Hopf algebra obtained from the stable-basis construction for Nakajima quiver varieties. Neguț's stable-basis realization conjecture. The map defined by the action product should yield an isomorphism

A≅Uq(g^Q).\mathcal A\cong U_q(\widehat{\mathfrak g}^Q).

This is proposed as an algebraic-geometric identification of the shuffle-algebra realization with the stable-basis quantum affine algebra. The text notes that choices of chambers, alcoves and polarization must be arranged so that the map lands in the target, and gives no resolution status.

References

Primary source

Andrei Neguţ, “Shuffle algebras for quivers and R-matrices”, arXiv:2109.14517 (2022).

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.