The abelian/nonabelian correspondence and Frobenius manifolds

• 成果类型: Article
• 署名作者: Ciocan-Fontanine, Ionut; Kim, Bumsig; Sabbah, Claude
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; Korea Institute for Advanced Study (KIAS); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; Ecole Polytechnique
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-007-0082-x
• 发表日期: 2008
• 页码: 301-343
• 关键词: quantum cohomology; conjecture

摘要

We propose an approach via Frobenius manifolds to the study (began in [BCK2] of the relation between rational Gromov-Witten invariants of nonabelian quotients X//G and those of the corresponding abelianized quotients X//T, for T a maximal torus in G. The ensuing conjecture expresses the Gromov-Witten potential of X//G in terms of the potential of X//T. We prove this conjecture when the nonabelian quotients are partial flag manifolds.