A coproduct structure on the formal affine Demazure algebra

TL;DR

This paper extends the coproduct structure on nil Hecke rings to a broader class of algebraic oriented cohomology theories and constructs an algebraic model for T-equivariant cohomology of flag varieties.

Contribution

It generalizes the coproduct structure to arbitrary algebraic oriented cohomology theories and develops an algebraic model for T-equivariant cohomology of flag varieties.

Findings

Generalized coproduct structure to arbitrary algebraic oriented cohomology theories.

Constructed an algebraic model for T-equivariant cohomology of complete flag varieties.

Extended the framework of nil Hecke rings to new algebraic contexts.

Abstract

In the present paper we generalize the coproduct structure on nil Hecke rings introduced and studied by Kostant-Kumar to the context of an arbitrary algebraic oriented cohomology theory and its associated formal group law. We then construct an algebraic model of the T-equivariant oriented cohomology of the variety of complete flags.