Quantum generalization of the Horn conjecture

Belkale, Prakash

doi:10.1090/S0894-0347-07-00584-X

Quantum generalization of the Horn conjecture
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by Prakash Belkale

J. Amer. Math. Soc. 21 (2008), 365-408

DOI: https://doi.org/10.1090/S0894-0347-07-00584-X

Published electronically: October 25, 2007

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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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