Quantum generalization of the Horn conjecture

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 ) (n) , (3) transversality statements for quantum Schubert calculus in any characteristic for the ordinary Grassmannians, (4) determination of the smallest power of q q in an arbitrary (small quantum) product of Schubert varieties in an ordinary Grassmannian.