Elliptic stable envelope for Hilbert scheme of points in the plane

TL;DR

This paper derives an explicit formula for the elliptic stable envelope of the Hilbert scheme of points on a complex plane, revealing a tree-structured sum over Young diagrams and connecting to K-theory and cohomology limits.

Contribution

It provides the first explicit elliptic stable envelope formula for the Hilbert scheme of points, structured as a sum over trees in Young diagrams.

Findings

Explicit elliptic stable envelope formula involving Young diagrams

Connections to K-theory and cohomology limits

Structured as a sum over trees in Young diagrams

Abstract

We find an explicit formula for the elliptic stable envelope in the case of the Hilbert scheme of points on a complex plane. The formula has a structure of a sum over trees in Young diagrams. In the limit we obtain the formulas for the stable envelope in equivariant $K$-theory (with arbitrary slope) and equivariant cohomology.