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Eigenvalues of Hermitian matrices and equivariant cohomology of Grassmannians
| Content Provider | Semantic Scholar |
|---|---|
| Author | Anderson, David L. T. Richmond, Edward Yong, Alexander |
| Copyright Year | 2012 |
| Abstract | The saturation theorem of [Knutson-Tao '99] concerns the nonvanishing of Littlewood-Richardson coefficients. In combination with work of [Klyachko '98], it implies [Horn '62]'s conjecture about eigenvalues of sums of Hermitian matrices. This eigenvalue problem has a generalization [Friedland '00] to majorized sums of Hermitian matrices. We further illustrate the common features between these two eigenvalue problems and their connection to Schubert calculus of Grassmannians. Our main result gives a Schubert calculus interpretation of Friedland's problem, via equivariant cohomology of Grassmannians. In particular, we prove a saturation theorem for this setting. Our arguments employ the aformentioned work together with [Thomas-Yong '12]. |
| Starting Page | 1569 |
| Ending Page | 1582 |
| Page Count | 14 |
| File Format | PDF HTM / HTML |
| DOI | 10.1112/S0010437X13007343 |
| Alternate Webpage(s) | https://arxiv.org/pdf/1210.5003v2.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
