Eigenvalues, invariant factors, highest weights, and Schubert calculus

William Fulton

Eigenvalues, invariant factors, highest weights, and Schubert calculus

Algebraic Geometry 2007-05-23 v3 Commutative Algebra Representation Theory

Authors: William Fulton

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.

Keywords

grassmannian varieties tensor product random matrix theory

Cite

@article{arxiv.math/9908012,
  title  = {Eigenvalues, invariant factors, highest weights, and Schubert calculus},
  author = {William Fulton},
  journal= {arXiv preprint arXiv:math/9908012},
  year   = {2007}
}

Comments

42 pages, AMSTeX, with Xy-pic. This is the final version, including corrections made in page proofs for publication as a Research/Expository article in Bull. Amer. Math. Soc

Eigenvalues, invariant factors, highest weights, and Schubert calculus

Abstract

Keywords

Cite

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