Eigenvalues, invariant factors, highest weights, and Schubert calculus

William Fulton

Eigenvalues, invariant factors, highest weights, and Schubert calculus

代数几何 2007-05-23 v3 交换代数表示论

作者: William Fulton

摘要

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.

关键词

grassmannian varieties tensor product random matrix theory

引用

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

备注

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

摘要

关键词

引用

备注

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