Loading...
Please wait, while we are loading the content...
Similar Documents
Eigenvalues of Hermitian matrices and equivariant cohomology of Grassmannians
| Content Provider | Scilit |
|---|---|
| Author | Anderson, David Richmond, Edward Yong, Alexander |
| Copyright Year | 2013 |
| Description | Journal: Compositio Mathematica The saturation theorem of Knutson and Tao concerns the nonvanishing of Littlewood–Richardson coefficients. In combination with work of Klyachko, it implies Horn’s conjecture about eigenvalues of sums of Hermitian matrices. This eigenvalue problem has a generalization to majorized sums of Hermitian matrices, due to S. Friedland. 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 aforementioned work together with recent work of H. Thomas and A. Yong. |
| Ending Page | 1582 |
| Starting Page | 1569 |
| ISSN | 00221295 |
| e-ISSN | 15705846 |
| DOI | 10.1112/s0010437x13007343 |
| Journal | Compositio Mathematica |
| Issue Number | 9 |
| Volume Number | 149 |
| Language | English |
| Publisher | Wiley-Blackwell |
| Publisher Date | 2013-09-01 |
| Access Restriction | Open |
| Subject Keyword | Journal: Compositio Mathematica Saturation Theorem Equivariant Cohomology Cohomology of Grassmannians Hermitian Matrices |
| Content Type | Text |
| Resource Type | Article |
| Subject | Algebra and Number Theory |
