Timeline for Horn's spectrum problem with random Hermitian matrices
Current License: CC BY-SA 3.0
7 events
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| Nov 25, 2015 at 18:34 | comment | added | Terry Tao | Actually, the inequalities in the compact operator case are simply the union of the inequalities in the finite dimensional cases: see for instance the paper of Bercovici, Li, and Timotin in ams.org/mathscinet-getitem?mr=2567501 , together with the references therein. | |
| Nov 25, 2015 at 18:25 | comment | added | Terry Tao | I'd like to mention that the initial solution to Horn's conjecture also relies heavily on Klyachko's paper "Stable bundles, representation theory and Hermitian operators", Selecta Math. (N.S.) 4 (1998), no. 3, 419–445, in addition to my paper with Knutson. (There have since been subsequent proofs of Horn's conjecture that avoid the difficult GIT machinery of Klyachko, though.) | |
| Nov 25, 2015 at 17:53 | answer | added | user75274 | timeline score: 3 | |
| Nov 25, 2015 at 15:50 | comment | added | Denis Serre | @Zoalroshd. For a reference, see my edits. The polytope his an exponentialcomplexity as $n\rightarrow+\infty$. Hence I doubt that it adapts easily to the case of a Hilbert space. | |
| Nov 25, 2015 at 15:48 | history | edited | Denis Serre | CC BY-SA 3.0 |
added 140 characters in body
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| Nov 25, 2015 at 15:32 | comment | added | BigM | I'm not expert in this field by no means and have a question rather than an insightful comment. Can you provide a link to Knutson & Tao's paper. I wonder if their answer changes if one replaces matrices with two self-adjoint compact operators on a separable Hilbert space. | |
| Nov 25, 2015 at 14:58 | history | asked | Denis Serre | CC BY-SA 3.0 |