Quantum Cohomology of Partial Flag Manifolds and a Residue Formula for Their Intersection Parings

TL;DR

This paper develops a residue formula for computing the equivariant quantum cohomology of partial flag manifolds, extending previous work and aiming to rigorously define these cohomological structures.

Contribution

It introduces a residue formula and explores behaviors of equivariant quantum cohomology for partial flag manifolds, providing a more rigorous foundation.

Findings

Residue formula for equivariant quantum cohomology

Behavioral analysis of quantum cohomology in flag manifolds

Extension of previous theoretical frameworks

Abstract

As a generalization of our previous paper [GK], we formulate a residue formula and some simple behaviors of equivariant quantum cohomology applying to compute the quantum cohomology of partial flag manifolds $F_{k_1,\cdots , k_l} $with a try to give a rigorous definition of equivariant quantum cohomology.