Timeline for Connection on a Hilbert bundle
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 10, 2021 at 20:52 | comment | added | André Henriques | The accepted answer to the following MO question is probably very relevant to the question you're asking: mathoverflow.net/questions/101526/… | |
| Jul 6, 2021 at 7:09 | vote | accept | Hasib | ||
| Jul 4, 2021 at 20:01 | comment | added | Yemon Choi | Naive question: is this bundle of Hilbert spaces what one gets by disintegrating the left regular rep of G over (some co-null subset of) the unitary dual? | |
| Jul 4, 2021 at 19:51 | answer | added | Dmitri Pavlov | timeline score: 3 | |
| Jul 4, 2021 at 17:18 | comment | added | Hasib | @DmitriPavlov: Fibres of the bundle are supposed to be the unitary irreducible representation spaces of the of the underlying Lie group. In this case, they are L^2(R^2, dx dy) or L^2(R, dx) depending on which sector of the unitary dual we are choosing. | |
| Jul 4, 2021 at 16:27 | comment | added | Dmitri Pavlov | @user78032: Is the bundle of Hilbert spaces finite-dimensional or infinite-dimensional? | |
| Jul 4, 2021 at 16:18 | comment | added | Hasib | @DmitriPavlov My topological group is a 7-dimensional nilpotent real Lie group which is topologically R^7. It's triple central extension of the abelian group of R^4 given in the paper:arxiv.org/pdf/1309.7086.pdf | |
| Jul 4, 2021 at 16:05 | comment | added | Dmitri Pavlov | @user78032: Is your topological group a real or complex Lie group, or do you also want to allow more general objects, such as p-adic groups? | |
| Jul 4, 2021 at 15:25 | comment | added | Hasib | Does it get any better if the base space can be topologized? In my case, the base space is the unitary dual of a locally compact topological group and is a topological space, say, equipped with Fell topology. It is a measure space equipped with the Plancherel measure. | |
| Jul 4, 2021 at 13:51 | comment | added | Alex M. | If it did, then one could do differential calculus in an only measurable context. While some tormented notions of differentiability can exist in non-smooth settings (the metric derivative, for instance), only measurability is probably too little to get anything useful. | |
| Jul 4, 2021 at 6:25 | review | Low quality posts | |||
| Jul 4, 2021 at 7:32 | |||||
| Jul 4, 2021 at 6:08 | history | asked | Hasib | CC BY-SA 4.0 |