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ISSN 1088-9485(online) ISSN 0273-0979(print)



Eigenvalues, invariant factors, highest weights, and Schubert calculus

Author: William Fulton
Journal: Bull. Amer. Math. Soc. 37 (2000), 209-249
MSC (2000): Primary 15A42, 22E46, 14M15; Secondary 05E15, 13F10, 14C17, 15A18, 47B07
Published electronically: April 5, 2000
MathSciNet review: 1754641
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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

Received by editor(s): July 1, 1999
Received by editor(s) in revised form: January 3, 2000
Published electronically: April 5, 2000
Additional Notes: The author was partly supported by NSF Grant #DMS9970435.
Article copyright: © Copyright 2000 American Mathematical Society

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