Inductive construction of stable envelopes

TL;DR

This paper provides a new inductive proof for the existence and uniqueness of stable envelopes in equivariant elliptic cohomology, and explores their specialization to equivariant K-theory, broadening the theoretical framework.

Contribution

It introduces a direct inductive method for constructing stable envelopes and extends the theory to include equivariant K-theory, enhancing previous approaches.

Findings

Established existence and uniqueness of stable envelopes via inductive proof

Extended the construction to equivariant K-theory

Clarified the relationship between elliptic cohomology and K-theory

Abstract

We revisit the construction of stable envelopes in equivariant elliptic cohomology [arXiv:1604.00423] and give a direct inductive proof of their existence and uniqueness in a rather general situation. We also discuss the specialization of this construction to equivariant K-theory.