Affine symmetries in quantum cohomology: corrections and new results

TL;DR

This paper corrects previous errors in the equivariant quantum cohomology formulas for homogeneous spaces and introduces new formulas in the equivariant homology of the affine Grassmannian, advancing understanding of affine symmetries.

Contribution

It provides corrected equivariant formulas for quantum cohomology and introduces new formulas in affine Grassmannian homology, enhancing the theoretical framework.

Findings

Corrected equivariant quantum cohomology formulas

New Pieri-type formulas in affine Grassmannian homology

Clarified affine symmetry structures in quantum cohomology

Abstract

In a previous paper Affine symmetries of the equivariant quantum cohomology of rational homogeneous spaces, a general formula was given for the multiplication by some special Schubert classes in the quantum cohomology of any homogeneous space. Although this formula is correct in the non equivariant setting, the stated equivariant version was wrong. We provide corrections for the equivariant formula, thus giving a correct argument for the non equivariant formula. We also give new formulas in the equivariant homology of the affine grassmannian that could lead to Pieri type formulas.