Elliptic stable envelopes

TL;DR

This paper constructs elliptic stable envelopes for Nakajima quiver varieties, generalizing previous results and applying them to compute monodromies of q-difference equations in enumerative K-theory.

Contribution

It introduces elliptic stable envelopes in equivariant elliptic cohomology, extending prior work and enabling new computations in quantum K-theory and related equations.

Findings

Elliptic stable envelopes are constructed for Nakajima quiver varieties.

The work generalizes previous stable envelope results to the elliptic setting.

Applications include computing monodromies of q-difference equations in enumerative K-theory.

Abstract

We construct stable envelopes in equivariant elliptic cohomology of Nakajima quiver varieties. In particular, this gives an elliptic generalization of the results of arXiv:1211.1287. We apply them to the computation of the monodromy of $q$-difference equations arising the enumerative K-theory of rational curves in Nakajima varieties, including the quantum Knizhnik-Zamolodchikov equations.