Timeline for Terminology for the "natural probability measure" on the set of irreducible characters of a finite group
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 2, 2022 at 20:31 | comment | added | Yemon Choi | Thanks @DanRomik | |
| May 2, 2022 at 18:26 | comment | added | Dan Romik | @YemonChoi I think it’s not so much that Wikipedia is inconsistent, but that the literature is inconsistent (in a way that is not uncommon to see in many emerging areas of research). But my impression — admittedly biased since I work in combinatorial probability — is that almost all the work on Plancherel measures has been in the context of finite groups, and almost all of that was on the specific case of the symmetric group. So as long as you make clear the context and include precise definitions, I think “Plancherel measure” is indeed the best term to use. | |
| May 2, 2022 at 15:55 | comment | added | Yemon Choi | @AnuragSahay yes, this is the result I mention in passing at the end of my question. I recommend the exposition in Folland's book on abstract harmonic analysis, if you have access to a copy. | |
| May 2, 2022 at 15:38 | comment | added | Yemon Choi | Although as @LSpice has pointed out, the wikipedia page is not consistent since the Plancherel measure they mention for compact groups is the "harmonic analyst's Plancherel measure" and differs from the definition they give above for finite groups. (Note that the difference cannot be rescued by rescaling Haar measure) | |
| May 2, 2022 at 15:36 | comment | added | Yemon Choi | Thanks @BenjaminSteinberg - well, I guess that is what I will have to use. This particular paper probably only deals with finite groups. | |
| May 2, 2022 at 15:32 | comment | added | LSpice | I agree that, contra Wikipedia, it would be confusing to call your measure Plancherel measure if your audience includes non-(finite-group theorists). Without explicit indication, I would expect the Haar measure for a finite group to be a special case of that for a compact group. | |
| May 2, 2022 at 15:28 | comment | added | Anurag Sahay | It never occurred to me before reading that Wikipedia page that the Plancherel measure was named after Plancherel directly. I always assumed there was some deeper connection to some type of non-commutative Plancherel's/Parseval's theorem (is there?). | |
| May 2, 2022 at 15:13 | comment | added | Benjamin Steinberg | I've always seem Plancherel measure. Wiki agrees en.m.wikipedia.org/wiki/Plancherel_measure | |
| May 2, 2022 at 15:09 | history | asked | Yemon Choi | CC BY-SA 4.0 |