On the big quantum cohomology of coadjoint varieties

TL;DR

This paper investigates the quantum cohomology of coadjoint varieties in simple algebraic groups, revealing their semisimplicity properties and connections to ADE-singularities across all Dynkin types.

Contribution

It determines the non-semisimple components of the small quantum cohomology and shows the big quantum cohomology is always generically semisimple.

Findings

Non-semisimple factors relate to ADE-singularities

Big quantum cohomology is generically semisimple

Small quantum cohomology is often not semisimple

Abstract

This paper is devoted to the study of the quantum cohomology of coadjoint varieties of simple algebraic groups across all Dynkin types. We determine the non-semisimple factors of the small quantum cohomology ring and relate them to ADE-singularities. Moreover, we show that the big quantum cohomology of a coadjoint variety is always generically semisimple even though in most cases the small quantum cohomology is not.