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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Degree bounds in quantum Schubert calculus


Author: Alexander Yong
Journal: Proc. Amer. Math. Soc. 131 (2003), 2649-2655
MSC (1991): Primary 14M15; Secondary 05E05, 14N10
Published electronically: January 8, 2003
MathSciNet review: 1974319
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Abstract: Fulton and Woodward have recently identified the smallest degree of $q$ that appears in the expansion of the product of two Schubert classes in the (small) quantum cohomology ring of a Grassmannian. We present a combinatorial proof of this result, and provide an alternative characterization of this smallest degree in terms of the rim hook formula for the quantum product.


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Additional Information

Alexander Yong
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: ayong@umich.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06850-3
PII: S 0002-9939(03)06850-3
Keywords: Gromov-Witten invariants, quantum cohomology, Grassmannian, Schubert calculus
Received by editor(s): December 14, 2001
Received by editor(s) in revised form: April 2, 2002
Published electronically: January 8, 2003
Communicated by: John R. Stembridge
Article copyright: © Copyright 2003 American Mathematical Society