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Journal of the American Mathematical Society

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

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Quantum generalization of the Horn conjecture
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by Prakash Belkale PDF
J. Amer. Math. Soc. 21 (2008), 365-408 Request permission

Abstract:

The following results are presented in this paper: (1) a quantum (multiplicative) generalization of the Horn conjecture which gives a recursive characterization of the possible eigenvalues of a product of unitary matrices, (2) the saturation conjecture for the fusion structure coefficients for SL$(n)$, (3) transversality statements for quantum Schubert calculus in any characteristic for the ordinary Grassmannians, (4) determination of the smallest power of $q$ in an arbitrary (small quantum) product of Schubert varieties in an ordinary Grassmannian.
References
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Additional Information
  • Prakash Belkale
  • Affiliation: Department of Mathematics, University of North Carolina–Chapel Hill, CB #3250, Phillips Hall, Chapel Hill, North Carolina 27599
  • MR Author ID: 684040
  • Email: belkale@email.unc.edu
  • Received by editor(s): July 22, 2005
  • Published electronically: October 25, 2007
  • Additional Notes: The author was partially supported by NSF grant DMS-0300356.
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 21 (2008), 365-408
  • MSC (2000): Primary 14N35, 14D20
  • DOI: https://doi.org/10.1090/S0894-0347-07-00584-X
  • MathSciNet review: 2373354