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Eigenvalues, invariant factors, highest weights, and Schubert calculus

Author(s): William Fulton
Journal: Bull. Amer. Math. Soc. 37 (2000), 209-249.
MSC (2000): Primary 15A42, 22E46, 14M15; Secondary 05E15, 13F10, 14C17, 15A18, 47B07
Posted: April 5, 2000
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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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Additional Information:

William Fulton
Affiliation: University of Michigan, Ann Arbor, MI 48109-1109
Email: wfulton@math.lsa.umich.edu

DOI: 10.1090/S0273-0979-00-00865-X
PII: S 0273-0979(00)00865-X
Received by editor(s): in July 1999 and in revised form January 3, 2000
Posted: April 5, 2000
Additional Notes: The author was partly supported by NSF Grant #DMS9970435.
Copyright of article: Copyright 2000, American Mathematical Society

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