On the quantum cohomology of adjoint varieties

TL;DR

This paper investigates the quantum cohomology of specific homogeneous spaces, revealing bounded quantum parameters, providing algebra presentations, and exploring duality properties, thus advancing understanding of their algebraic structures.

Contribution

It offers new presentations of quantum cohomology algebras for adjoint varieties and analyzes their semi-simplicity and duality properties.

Findings

Quantum product involves powers of the quantum parameter up to 2.

Presented algebraic structures of quantum cohomology for certain varieties.

Identified semi-simplicity and duality features in these algebras.

Abstract

We study the quantum cohomology of quasi-minuscule and quasi-cominuscule homogeneous spaces. The product of any two Schubert cells does not involve powers of the quantum parameter higher than 2. With the help of the quantum to classical principle we give presentations of the quantum cohomology algebras. These algebras are semi-simple for adjoint non coadjoint varieties and some properties of the induced strange duality are shown.