Eigenvalues, invariant factors, highest weights, and Schubert calculus

Fulton, William

doi:10.1090/S0273-0979-00-00865-X

Eigenvalues, invariant factors, highest weights, and Schubert calculus
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Bull. Amer. Math. Soc. 37 (2000), 209-249 Request permission

Abstract:

We describe recent work of Klyachko, Totaro, Knutson, and Tao that characterizes eigenvalues of sums of Hermitian matrices and decomposition of tensor products of representations of $GL_{n}(\mathbb {C})$. We explain related applications to invariant factors of products of matrices, intersections in Grassmann varieties, and singular values of sums and products of arbitrary matrices.

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