Quantum generalization of the Horn conjecture

Belkale, Prakash¹

¹ Department of Mathematics, University of North Carolina–Chapel Hill, CB #3250, Phillips Hall, Chapel Hill, North Carolina 27599

Journal of the American Mathematical Society, Tome 21 (2008) no. 2, pp. 365-408

Résumé

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.

Détail

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

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