UZH-Logo

Maintenance Infos

Quantum cohomology of the Lagrangian Grassmannian


Kresch, A; Tamvakis, H (2003). Quantum cohomology of the Lagrangian Grassmannian. Journal of Algebraic Geometry, 12(4):777-810.

Abstract

Let V be a symplectic vector space and LG be the Lagrangian Grassmannian which parametrizes maximal isotropic subspaces in V. We give a presentation for the (small) quantum cohomology ring QH∗ (LG) and show that its multiplicative structure is determined by the ring of Q-polynomials. We formulate a 'quantum Schubert calculus' which includes quantum Pieri and Giambelli formulas, as well as algorithms for computing the structure constants appearing in the quantum product of Schubert classes.

Let V be a symplectic vector space and LG be the Lagrangian Grassmannian which parametrizes maximal isotropic subspaces in V. We give a presentation for the (small) quantum cohomology ring QH∗ (LG) and show that its multiplicative structure is determined by the ring of Q-polynomials. We formulate a 'quantum Schubert calculus' which includes quantum Pieri and Giambelli formulas, as well as algorithms for computing the structure constants appearing in the quantum product of Schubert classes.

Citations

29 citations in Web of Science®
28 citations in Scopus®
Google Scholar™

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:2003
Deposited On:29 Nov 2010 16:26
Last Modified:05 Apr 2016 13:25
Publisher:University Press, Inc.
ISSN:1056-3911
Official URL:http://www.ams.org/journals/jag/2003-12-04/S1056-3911-03-00347-3
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1051.53070
http://www.ams.org/mathscinet-getitem?mr=1993764

Download

Full text not available from this repository.

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations