On the big quantum cohomology of coadjoint varieties

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.

v2: introduction is made more precise, sections 2-4 are reorganised and clarified, section 9 added, results remain unchanged

References in corpus (3)

• Cluster X-varieties, amalgamation and Poisson-Lie groups
• Semisimple quantum cohomology of some Fano varieties
• Towards a Littlewood-Richardson rule for Kac-Moody homogeneous spaces