Classical aspects of quantum cohomology of generalized flag varieties

TL;DR

This paper reveals that many genus zero Gromov-Witten invariants for flag varieties are equivalent to classical intersection numbers of Schubert cycles, bridging quantum and classical cohomology.

Contribution

It demonstrates the equivalence of certain quantum invariants with classical intersection numbers in the context of generalized flag varieties.

Findings

Genus zero Gromov-Witten invariants coincide with classical intersection numbers.

Many invariants for different homology classes are identical.

The results connect quantum cohomology with classical Schubert calculus.

Abstract

We show that various genus zero Gromov-Witten invariants for flag varieties representing different homology classes are indeed the same. In particular, many of them are classical intersection numbers of Schubert cycles.