Header

UZH-Logo

Maintenance Infos

Quantum Pieri rules for isotropic Grassmannians


Buch, A S; Kresch, A; Tamvakis, H (2009). Quantum Pieri rules for isotropic Grassmannians. Inventiones Mathematicae, 178(2):345-405.

Abstract

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.

Abstract

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.

Statistics

Citations

Dimensions.ai Metrics
31 citations in Web of Science®
30 citations in Scopus®
75 citations in Microsoft Academic
Google Scholar™

Altmetrics

Downloads

43 downloads since deposited on 04 Feb 2010
11 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2009
Deposited On:04 Feb 2010 13:55
Last Modified:18 Feb 2018 00:08
Publisher:Springer
ISSN:0020-9910
Additional Information:The original publication is available at www.springerlink.com
OA Status:Green
Publisher DOI:https://doi.org/10.1007/s00222-009-0201-y
Related URLs:http://arxiv.org/abs/0809.4966

Download