Existence and orthogonality of stable envelopes for bow varieties

Abstract

Stable envelopes, introduced by Maulik and Okounkov, provide a family of bases for the equivariant cohomology of symplectic resolutions. The theory of stable envelopes provides a fascinating interplay between geometry, combinatorics and integrable systems. In this expository article, we give a self-contained introduction to cohomological stable envelopes of type A bow varieties (an interesting class of varieties extending Nakajima quiver varieties). Our main focus is on the existence and the orthogonality properties of stable envelopes for bow varieties. The restriction to this specific class of varieties allows us to illustrate the theory combinatorially and to provide simplified proofs, both laying a basis for explicit calculations.