Timeline for Discrete-compact duality for nonabelian groups
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 22, 2011 at 5:22 | comment | added | Marc Palm | I just tried to mention an example, which shows how little one knows for general discrete groups and also why vNa decomposition is probably not the best interpretation for discrete groups, since the spectrum of the free group is only one point, and it's not clear if it is the "same" point for all free groups. Does this make sense? | |
| Jul 22, 2011 at 5:18 | history | edited | Marc Palm | CC BY-SA 3.0 |
deleted 37 characters in body
|
| Jul 21, 2011 at 21:30 | comment | added | Yemon Choi | Lastly, I don't see why the free group factor problem is relevant to (decomposition into) irreducible representations | |
| Jul 21, 2011 at 21:28 | comment | added | Yemon Choi | I also find the claim "Usually people talk say that the classification is just feasible for type 1 groups, which are nice to describe" somewhat unclear. (The unitary dual of certain p-adic Type I groups is, as far as I am aware, rather complicated) | |
| Jul 21, 2011 at 21:27 | comment | added | Yemon Choi | It has long been known that for type II groups, attempts to decompose representations as direct integrals of irreducibles. This can be seen in Robert's LMSLN book (I seem to remember linking to this somewhere else on MO< but I forget where). | |
| Jul 21, 2011 at 18:23 | history | edited | Marc Palm | CC BY-SA 3.0 |
added 168 characters in body
|
| Jul 21, 2011 at 15:57 | history | edited | Marc Palm | CC BY-SA 3.0 |
added 147 characters in body
|
| Jul 21, 2011 at 15:50 | history | edited | Marc Palm | CC BY-SA 3.0 |
added 203 characters in body; added 51 characters in body
|
| Jul 19, 2011 at 12:42 | comment | added | Qiaochu Yuan | This seems like a fairly concrete sense in which what I asked for is true; thanks for this answer. I am curious whether there is a noncompact group with discrete dual in this sense, though. | |
| Jul 19, 2011 at 12:33 | history | edited | Marc Palm | CC BY-SA 3.0 |
added 27 characters in body
|
| Jul 19, 2011 at 12:22 | history | edited | Marc Palm | CC BY-SA 3.0 |
added 272 characters in body; edited body
|
| Jul 19, 2011 at 12:17 | history | answered | Marc Palm | CC BY-SA 3.0 |