Eigenvalues, invariant factors, highest weights, and Schubert calculus

Details Eigenvalues, invariant factors, highest weights, and Schubert calculus Eigenvalues, invariant factors, highest weights, and Schubert calculus

1999-08-02

arxiv.org/abs/math/9908012v3

Mathematics

Algebraic Geometry

42 pages, AMSTeX, with Xy-pic. This is the final version, including corrections made in page proofs for publication as a Resea

Scientific paper

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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