Timeline for Unitarizability of group representations
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 8, 2015 at 18:48 | comment | added | Yemon Choi | OK, thanks, I see from Wikipedia en.wikipedia.org/wiki/Harish-Chandra_module what you mean (but unfortunately can't help with the question) | |
| Jul 8, 2015 at 16:57 | comment | added | asv | @YemonChoi: As a first step, you may think about the usual isomorphism of representations you mentioned. However I do not insist to restrict to that notion. For example for representations of real reductive groups there is a notion of Harish-Chandra module which has no topology. Thus two Banach representations are called equivalent if they have isomorphic (in the usual sense) Harish-Chandra modules. | |
| Jul 8, 2015 at 16:44 | comment | added | Yemon Choi | Probably I am confused because I think about Banach-space representations of arbitrary discrete groups more often than I do about representations of Lie algebras. Could you give me an example of an isometric representation of a group on some not-TVS-isomorphic-to-Hilbert Banach space, which is equivalent in your sense to a unitary representation of this group? | |
| Jul 8, 2015 at 16:03 | comment | added | asv | @YemonChoi: as I mentioned in the post, I do not have in mind any particular kind of equivalence. Also a priori (say in the case of reductive groups) I would not like to assume that the Banach space is isomorphic to Hilbert. | |
| Jul 8, 2015 at 14:53 | comment | added | Yemon Choi | Could you please be a bit more precise about what notion of equiavalence you have in mind? In particular, are you demanding that your Banach space is isomorphic (in the TVS category) to a Hilbert space? | |
| Jul 8, 2015 at 10:31 | history | asked | asv | CC BY-SA 3.0 |