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

 

Quantum double Schubert polynomials represent Schubert classes


Authors: Thomas Lam and Mark Shimozono
Journal: Proc. Amer. Math. Soc. 142 (2014), 835-850
MSC (2010): Primary 14N35; Secondary 14M15
Published electronically: December 11, 2013
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Abstract: The quantum double Schubert polynomials studied by Kirillov and Maeno, and by Ciocan-Fontanine and Fulton, are shown to represent Schubert classes in Kim's presentation of the equivariant quantum cohomology of the flag variety. Parabolic analogues of quantum double Schubert polynomials are introduced and shown to represent Schubert classes in the equivariant quantum cohomology of partial flag varieties. This establishes a new method for computing equivariant Gromov-Witten invariants for partial flag varieties. For complete flags Anderson and Chen have announced a proof with different methods.


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Additional Information

Thomas Lam
Affiliation: Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, Michigan 48109
Email: tfylam@umich.edu

Mark Shimozono
Affiliation: Department of Mathematics, MC0151, 460 McBryde Hall, Virginia Tech, 225 Stanger Street, Blacksburg, Virginia 24061
Email: mshimo@vt.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11831-9
PII: S 0002-9939(2013)11831-9
Received by editor(s): October 22, 2011
Received by editor(s) in revised form: April 17, 2012
Published electronically: December 11, 2013
Additional Notes: The first author was supported by NSF grant DMS-0901111 and by a Sloan Fellowship.
The second author was supported by NSF DMS-0652641 and DMS-0652648.
Communicated by: Lev Borisov
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.