Condensed Matter

In a joint work with Yalong Cao, Andrei Okounkov, and Zijun Zhou, we introduce stable envelopes in critical cohomology and K-theory for symmetric quiver varieties with potentials and related geometries.

 

Critical stable envelopes are compatible with dimensional reductions, specializations, Hall products, and other geometric constructions. In particular, for tripled quivers with canonical cubic potentials, critical stable envelopes

reproduce those on Nakajima quiver varieties, constructed by Maulik and Okounkov.

 

Using the critical stable envelopes, we can construct solutions to Yang-Baxter equations with R-matrixes acting on the critical cohomologies of symmetric quiver varieties with potentials. Then, the FRT formalism gives natural (shifted) (super) Yangian action on these critical cohomologies.