Quantum Pieri rules for isotropic Grassmannians

• 成果类型: Article
• 署名作者: Buch, Anders Skovsted; Kresch, Andrew; Tamvakis, Harry
• 署名单位: University System of Maryland; University of Maryland College Park; Rutgers University System; Rutgers University New Brunswick; University of Zurich
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-009-0201-y
• 发表日期: 2009
• 页码: 345-405
• 关键词: orthogonal grassmannians; COHOMOLOGY; FORMULA; THEOREM

摘要

We study the three point genus zero Gromov-Witten invariants on the Grassmannians which parametrize non-maximal isotropic subspaces in a vector space equipped with a nondegenerate symmetric or skew-symmetric form. We establish Pieri rules for the classical cohomology and the small quantum cohomology ring of these varieties, which give a combinatorial formula for the product of any Schubert class with certain special Schubert classes. We also give presentations of these rings, with integer coefficients, in terms of special Schubert class generators and relations.