Timeline for Is there "Schur-Weyl duality" for infinite dimensional unitary group?
Current License: CC BY-SA 3.0
11 events
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| Mar 7, 2012 at 21:38 | comment | added | Julien Melleray | @Alexander: Todor speaks about the strong operator topology. Finite-dimensional perturbations of identity are dense because a basic open set only "names" finitely many vectors. Anyway, as he proved in the paper he links to, continuity assumptions can be dropped when one considers representations on a separable space. | |
| Mar 7, 2012 at 21:19 | vote | accept | Michał Oszmaniec | ||
| Mar 7, 2012 at 21:19 | history | bounty ended | Michał Oszmaniec | ||
| Mar 7, 2012 at 15:22 | comment | added | Alexander Chervov | @Todor why dense ? In what topology ? direct limit - operators of the form 1+K , K - finite-dim. you cannot approximate $e^{ia} Id$ by this operators if we speak about norm-topology. | |
| Mar 5, 2012 at 9:09 | comment | added | Todor Tsankov | I should have also mentioned that the direct limit of the finite-dimensional groups is dense in $U(\mathcal{H})$. | |
| Mar 4, 2012 at 18:34 | comment | added | Alexander Chervov | @Todor But restriction and extension does not mean equvivalence of irreps. I mean when you restrict irrep you can get reducible, as well as, when you extend non-equiv. irreps. you can get equiv reps. As far as I remember it is always emphasized that the two groups: 1) U(H) and 2) limit U(n) has very different rep. theory. – Alexander Chervov | |
| Mar 4, 2012 at 16:35 | history | edited | Todor Tsankov | CC BY-SA 3.0 |
added 365 characters in body
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| Mar 4, 2012 at 16:19 | comment | added | Todor Tsankov | I am not sure I understand your comment. Every representation of the infinite-dimensional unitary group restricts to a representation of the direct limit of finite-dimenssional unitary groups and conversely, each of the representations they consider extends to one of the full unitary group. | |
| Mar 4, 2012 at 13:47 | comment | added | Anatoly Kochubei | Meanwhile, indeed, for the subgroup considered by Kirillov, there is a relation of the requested kind. | |
| Mar 4, 2012 at 13:34 | comment | added | Anatoly Kochubei | As I wrote in my answer, the paper you cite are not about the whole unitary group. As for the results, see the quotation from Olhanski himself in my answer. | |
| Mar 4, 2012 at 13:20 | history | answered | Todor Tsankov | CC BY-SA 3.0 |