Structure Constants in equivariant oriented cohomology of flag varieties

TL;DR

This paper derives algebraic formulas for structure constants in equivariant oriented cohomology of flag varieties, unifying and extending known results in cohomology, K-theory, and stable bases.

Contribution

It provides a new algebraic approach to compute structure constants, generalizing and recovering several classical formulas in geometry.

Findings

Derived a formula for structure constants in equivariant oriented cohomology.

Unified formulas for Schubert classes in cohomology and K-theory.

Obtained a formula for K-theoretic stable basis.

Abstract

We obtain a formula for structure constants of certain variant form of Bott-Samelson classes for equivariant oriented cohomology of flag varieties. Specializing to singular cohomology/K-theory, we recover formulas of structure constants of Schubert classes of Goldin-Knutson, and that of structure constants of Segre-Schwartz-MacPherson classes of Su. We also obtain a formula for K-theoretic stable basis. Our method comes from the study of formal affine Demazure algebra, so is purely algebraic, while the above mentioned results are geometric.