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

 

Branching Schubert calculus and the Belkale-Kumar product on cohomology


Authors: Nicolas Ressayre and Edward Richmond
Journal: Proc. Amer. Math. Soc. 139 (2011), 835-848
MSC (2010): Primary 14M15, 14N15; Secondary 57T15
Published electronically: October 1, 2010
MathSciNet review: 2745636
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Abstract: In 2006 Belkale and Kumar defined a new product on the cohomology of flag varieties and used this new product to give an improved solution to the eigencone problem for complex reductive groups. In this paper, we give a generalization of the Belkale-Kumar product to the branching Schubert calculus setting. The study of branching Schubert calculus attempts to understand the induced map on cohomology of an equivariant embedding of flag varieties. The main application of our work is a compact formulation of the solution to the branching eigencone problem.


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Additional Information

Nicolas Ressayre
Affiliation: Département de Mathématiques, Université Montpellier II, Case courrier 051-Place Eugène Bataillon, 34095 Montpellier Cedex 5, France
Email: ressayre@math.univ-montp2.fr

Edward Richmond
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97402
Address at time of publication: Department of Mathematics, University of British Columbia, Vancouver, BC, V6T172, Canada
Email: erichmo2@uoregon.edu, erichmond@math.ubc.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10681-0
PII: S 0002-9939(2010)10681-0
Keywords: Schubert calculus, Belkale-Kumar product, eigencone, structure constants
Received by editor(s): September 16, 2009
Received by editor(s) in revised form: February 27, 2010, and April 9, 2010
Published electronically: October 1, 2010
Additional Notes: The first author was partially supported by the French National Research Agency (ANR-09-JCJC-0102-01).
Communicated by: Ted Chinburg
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.