Affine symmetries of the equivariant quantum cohomology ring of rational homogeneous spaces

Simple item page
dc.creatorChaput, Pierre-Emmanuel
dc.creatorManivel, Laurent
dc.creatorPerrin, Nicolas
dc.date2007-12-19
dc.date.accessioned2026-07-07T08:50:18Z
dc.date.available2026-07-07T08:50:18Z
dc.descriptionLet $X$ be a rational homogeneous space and let $QH^*(X)_{loc}^\times$ be the group of invertible elements in the small quantum cohomology ring of $X$ localised in the quantum parameters. We generalise results of arXiv:math/0609796 and realise explicitly the map $π_1({\rm Aut}(X))\to QH^*(X)_{loc}^\times$ described in arXiv:dg-ga/9511011. We even prove that this map is an embedding and realise it in the equivariant quantum cohomology ring $QH^*_T(X)_{loc}^\times$. We give explicit formulas for the product by these elements. The proof relies on a generalisation, to a quotient of the equivariant homology ring of the affine Grassmannian, of a formula proved by Peter Magyar arXiv:0705.3826. It also uses Peterson's unpublished result -- recently proved by Lam and Shimozono in arXiv:0705.1386 -- on the comparison between the equivariant homology ring of the affine Grassmannian and the equivariant quantum cohomology ring.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/0712.3131
dc.identifierhttp://arxiv.org/abs/0712.3131
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144563
dc.subjectAlgebraic Geometry
dc.subjectRepresentation Theory
dc.subject14M15, 14N35
dc.titleAffine symmetries of the equivariant quantum cohomology ring of rational homogeneous spaces
dc.typetext

Files

Collections

arXiv