On the quantum cohomology of adjoint varieties

Pierre-Emmanuel Chaput (1) , Nicolas Perrin (2)

1 IECN - Institut Élie Cartan de Nancy
2 HCM - Hausdorff Center for Mathematics

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.

Mots clés: Quantum Cohomology; Adjoint varieties

Domaines: Géométrie algébrique [math.AG]

Pierre-Emmanuel Chaput, Nicolas Perrin. On the quantum cohomology of adjoint varieties. Proceedings of the London Mathematical Society, 2011, 103 (2), pp.294-330. ⟨10.1112/plms/pdq052⟩. ⟨hal-01256756⟩