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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Quantum generalization of the Horn conjecture


Author: Prakash Belkale
Journal: J. Amer. Math. Soc. 21 (2008), 365-408
MSC (2000): Primary 14N35, 14D20
Published electronically: October 25, 2007
MathSciNet review: 2373354
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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.


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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
Email: belkale@email.unc.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-07-00584-X
PII: S 0894-0347(07)00584-X
Received by editor(s): July 22, 2005
Published electronically: October 25, 2007
Additional Notes: The author was partially supported by NSF grant DMS-0300356.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.