Localized operations on T-equivariant oriented cohomology of projective homogeneous varieties

TL;DR

This paper develops a general algorithm for computing multiplicative cohomological operations on T-equivariant oriented cohomology of projective homogeneous varieties, extending previous methods and utilizing equivariant Schubert calculus techniques.

Contribution

It introduces a comprehensive algorithm for T-equivariant operations on algebraic oriented cohomology, generalizing prior approaches and demonstrating their compatibility with classical operators.

Findings

Extended operations to T-equivariant theories.

Provided explicit computation methods using Schubert calculus.

Showed operations of additive type commute with push-pull operators.

Abstract

In the present paper we provide a general algorithm to compute multiplicative cohomological operations on algebraic oriented cohomology of projective homogeneous G-varieties, where G is a split reductive algebraic group over a field of characteristic 0. More precisely, we extend such operations to the respective T-equivariant (T is a maximal split torus of G) oriented theories, and then compute them using equivariant Schubert calculus techniques. This generalizes an approach suggested by Garibaldi-Petrov-Semenov for Steenrod operations. We also show that operations on the theories of additive type commute with classical push-pull operators up to a twist.