Timeline for $F$ symbols for finite groups
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Sep 1, 2020 at 20:32 | comment | added | Student | There is a draft put online in 2015 concerning 3j and 6j symbols for finite groups with $dimHom(A,BC)=1$. What doesn't make sense to me is also the arbitrariness of the choice of basis.. I'd love to discuss further if you wish. | |
| Jan 26, 2017 at 6:50 | comment | added | Allen Knutson | Yep, same issue: how to pick these bases? In particular, if you and some author pick them differently, then their table won't be good for you. For $SU(2)$ everybody knows how to do this. For other connected Lie groups one can in principle use Lusztg's extremely-difficult-to-compute canonical basis. For general finite groups there's nothing analogous. | |
| Jan 25, 2017 at 11:46 | comment | added | Raul Santos | Allen, thanks for your input. I am a little puzzled now. In principle, I can take the Clebsch-Gordan coefficients of a tensor decomposition and use them to compute the $6j$ symbols. This amounts to choose a basis of $A\otimes B$. Tensoring the result with another representation in $C$, and computing the Clebsch-Gordan coefficients, will give me a basis of $(A\otimes B)\otimes C$. Doing the same in the opposite order gives a basis in $A\otimes(B\otimes C)$. Comparing the two should give the $6j$. A related thread in which you also participated is mathoverflow.net/q/15800/103992 | |
| Jan 24, 2017 at 12:03 | comment | added | Allen Knutson | I doubt it. $6j$ is about decomposing $A\otimes B\otimes C$ in two different ways, and the crucial thing about $SU(2)$ is that inside a tensor product $A\otimes B$ of irreps, each $D$ occurs at most once. So you get, essentially, two different canonical bases of $Hom(D,A\otimes B\otimes C)$ and $6j$ compares them. This multiplicity-freeness won't hold for almost any nonabelian finite groups. | |
| S Jan 24, 2017 at 11:14 | history | suggested | Hee Kwon Lee | CC BY-SA 3.0 |
dollar is needed for math expression
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| Jan 24, 2017 at 11:00 | review | Suggested edits | |||
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| Jan 24, 2017 at 10:36 | review | First posts | |||
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| Jan 24, 2017 at 10:34 | history | asked | Raul Santos | CC BY-SA 3.0 |