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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Branching Schubert calculus and the Belkale-Kumar product on cohomology
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by Nicolas Ressayre and Edward Richmond PDF
Proc. Amer. Math. Soc. 139 (2011), 835-848 Request permission

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
  • MR Author ID: 875224
  • Email: erichmo2@uoregon.edu, erichmond@math.ubc.ca
  • 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
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 835-848
  • MSC (2010): Primary 14M15, 14N15; Secondary 57T15
  • DOI: https://doi.org/10.1090/S0002-9939-2010-10681-0
  • MathSciNet review: 2745636