On the big quantum cohomology of coadjoint varieties

2021/12/23 by Nicolas Perrin, Perrin, Nicolas, Maxim Smirnov +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Symplectic Geometry (math.SG) #math.AG #math.RA #math.SG

paper · pdf · doi:10.48550/arxiv.2112.12436

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

openalex publication_date 2021/12/23 · arxiv created 2022/04/12 · arxiv updated 2022/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Update on quantum cohomology of IG(2,2n)
• Towards a Littlewood-Richardson rule for Kac-Moody homogeneous spaces
• Semisimple quantum cohomology of some Fano varieties
• Cluster X-varieties, amalgamation and Poisson-Lie groups

Cited by

• A-D-E diagrams, Hodge--Tate hyperplane sections and semisimple quantum cohomology

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