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Eigenvalues, invariant factors, highest weights, and Schubert calculus

William Fulton
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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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William Fulton. 2000-03-27. Eigenvalues, invariant factors, highest weights, and Schubert calculus. https://arxiv.org/abs/math/9908012

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