Nil-Hecke rings and the Schubert calculus

TL;DR

This paper provides a comprehensive overview of Nil-Hecke algebra techniques applied to the equivariant Schubert calculus, extending their use to non-crystallographic root systems and K-theory of flag varieties.

Contribution

It offers a self-contained exposition on Nil-Hecke algebra methods in Schubert calculus and demonstrates their application beyond crystallographic systems.

Findings

Extended Nil-Hecke techniques to non-crystallographic root systems

Applied methods to (connective) K-theory of flag varieties

Provided a self-contained exposition for broader accessibility

Abstract

The purpose of the present notes is to give a self-contained exposition on the use of the techniques of Nil-Hecke algebras in the localization approach to the equivariant Schubert calculus for cohomology of flag varieties. We also demonstrate how these techniques can be applied to non-crystallographic root systems as well as to study (connective) $K$-theory of flag varieties.