Timeline for On self-dual group-subgroup subfactors
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Feb 12, 2021 at 1:21 | history | edited | Sebastien Palcoux | CC BY-SA 4.0 |
forgot unital
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| Jun 15, 2016 at 16:59 | comment | added | Sebastien Palcoux | @MarcelBischoff: No, see the answer here: mathoverflow.net/q/242271/34538 | |
| Jun 13, 2016 at 19:14 | comment | added | Marcel Bischoff | Ok, I see, I was already expecting that this is automatic. Is $G$ necessarily abelian? | |
| Jun 13, 2016 at 19:11 | comment | added | Sebastien Palcoux | @MarcelBischoff: It is a Gelfand pair in this case because $\forall h_1, h_2, h_3 \in H \subset G\rtimes H$ and $\forall g,g' \in G \subset G\rtimes H$, we have: $$ h_1gh_2g'h_3 = h_1 g \sigma_{h_2}(g') h_2 h_3 = h_1 \sigma_{h_2}(g') g h_2 h_3 = h_1 h_2 g' h_2^{-1} g h_2h_3 $$ which means that $HgHg'H = Hg'HgH$, i.e. the double coset algebra is commutative. | |
| Jun 13, 2016 at 18:19 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
No, no, no..., A_4 is not abelian!!!
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| Jun 13, 2016 at 18:04 | comment | added | Marcel Bischoff | It is necessary, that the double coset algebra $H\backslash (G\rtimes H) /H$ is commutative, i.e. $(G\rtimes H,H)$ has to be a Gelfand pair. Namely, one two box space is $\mathbb{C}^N$ where $N$ is the number of double cosets, while the other is the double coset algebra itself. | |
| Jun 13, 2016 at 18:03 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
This form is not sufficient. Is it necessary.
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| Jun 11, 2016 at 15:47 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
edited body
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| Jun 11, 2016 at 15:40 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
added 135 characters in body
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| Jun 11, 2016 at 15:34 | history | asked | Sebastien Palcoux | CC BY-SA 3.0 |