A geometric proof of an equivariant Pieri rule for flag manifolds

TL;DR

This paper provides a geometric proof of an equivariant Pieri rule for flag manifolds, offering an alternative to Robinson's algebraic proof and enhancing understanding through geometric methods.

Contribution

The paper introduces a geometric proof of the equivariant Pieri rule, complementing Robinson's algebraic approach and deepening the geometric understanding of flag manifold cohomology.

Findings

Geometric proof of the equivariant Pieri rule

Enhanced understanding of flag manifold cohomology

Alternative approach to algebraic proofs

Abstract

We use geometry to give a short proof of an equivariant Pieri rule in the classical flag manifold. This rule is due to Robinson, who gave an algebraic proof.