Timeline for Analogy between product of conjugacy classes and irreps: is there analog of Thompson conjecture ?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 5, 2017 at 21:52 | answer | added | Marty Isaacs | timeline score: 13 | |
| Sep 8, 2017 at 19:03 | vote | accept | Alexander Chervov | ||
| Aug 30, 2017 at 14:27 | answer | added | Jay Taylor | timeline score: 13 | |
| Aug 30, 2017 at 14:05 | comment | added | Jay Taylor | @PaulBroussous Thanks for clarifying. My comment was a reaction to reading this statement at the end of their article. I'll develop my comments into a proper answer. | |
| Aug 30, 2017 at 9:28 | comment | added | Paul Broussous | @Jay Taylor The answer to Alexander's question is indeed "no", but this is not due to this property of the Setinberg representation proved in arxiv.org/abs/1209.1768. This is due to the more precise fact proved in loc. cit.: for finite simple groups G, there exists an irrep $\pi$ which does not occur in the square of the regular representation by conjugation. So Heide, Saxi, Tiep and Zalesski prove the in fact stronger fact. It is false that for all $G$ and all irrep $\pi$, there exists an irrep $\chi$ such that $\pi$ occurs in $\chi\otimes {\bar \chi}$. | |
| Aug 30, 2017 at 8:33 | comment | added | Alexander Chervov | @JayTaylor Thank you very much ! I would suggest convert comments to an answer, may adding some details | |
| Aug 28, 2017 at 17:33 | comment | added | Jay Taylor | Actually the answer to your question is no for those special unitary groups. | |
| Aug 28, 2017 at 17:31 | comment | added | Jay Taylor | For finite simple groups of Lie type it is in fact the case that every (ordinary) irreducible character occurs in the square of the Steinberg character, except for some special unitary groups. This was proved by Heide, Saxl, Tiep, and Zalesski - arxiv.org/abs/1209.1768. | |
| Aug 28, 2017 at 17:03 | history | asked | Alexander Chervov | CC BY-SA 3.0 |