Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Quantum cohomology of the Lagrangian Grassmannian


Authors: Andrew Kresch and Harry Tamvakis
Journal: J. Algebraic Geom. 12 (2003), 777-810
DOI: https://doi.org/10.1090/S1056-3911-03-00347-3
Published electronically: June 3, 2003
MathSciNet review: 1993764
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Abstract | References | Additional Information

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 $\widetilde{Q}$-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.


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Additional Information

Andrew Kresch
Affiliation: Department of Mathematics, University of Pennsylvania, 209 South 33rd St., Philadelphia, Pennsylvania 19104-6395
Email: kresch@math.upenn.edu

Harry Tamvakis
Affiliation: Department of Mathematics, University of Pennsylvania, 209 South 33rd St., Philadelphia, Pennsylvania 19104-6395
Address at time of publication: Department of Mathematics, Brandeis University, P. O. Box 9110, MS 050, Waltham, Massachusetts 02454-9110
Email: harryt@math.upenn.edu, harryt@brandeis.edu

DOI: https://doi.org/10.1090/S1056-3911-03-00347-3
Received by editor(s): May 27, 2001
Published electronically: June 3, 2003

American Mathematical Society