A Pieri-type Formula for the Equivariant Cohomology of the Flag Manifold

TL;DR

This paper presents a combinatorial formula for structure constants in the T-equivariant cohomology of the flag manifold, extending classical Pieri formulas and applying to double Schubert polynomials.

Contribution

It provides the first explicit Pieri-type formula for T-equivariant cohomology of flag manifolds, generalizing previous results in ordinary cohomology.

Findings

Explicit combinatorial formula derived for structure constants

Generalizes Sottile's 1996 Pieri formula to equivariant setting

Applicable to double Schubert polynomials

Abstract

We prove an explicit combinatorial formula for certain structure constants of the T-equivariant cohomology of the flag manifold SLn/B. Our result generalizes the Pieri-type formula in ordinary cohomology proved by Sottile in 1996. Our result also gives a Pieri-type formula for the double Schubert polynomials introduced by Lascoux and Schutzenberger.