Representations of alternating group of degree 4 #43
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lkdvos
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lkdvos
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Looks like a great start!
In general it looks like most of the implementations really assume N = 4 and are not at all expected to work for anything else, this is completely fine, but the signatures should then be made more specific as well.
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So, I read a bit more about the representation theory of the alternating groups, and there are a couple points that I want to revisit. The first is that if we want this to really be Therefore I would kind of like to suggest an alternative, where we simply define I'm happy to have a go at this tomorrow if you don't object to this. |
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I have also been wondering about this and fully agree with Lukas' analysis, and the decision of simply restricting to |
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Seems reasonable. Feel free to go for it! |
borisdevos
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Co-authored-by: Lukas Devos <[email protected]>
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I will add the intertwiner test tomorrow :) |
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That's actually really cool that just works, thanks for implementing! |
lkdvos
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lkdvos
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Thanks for the work, this PR looks great to me!
@Jutho, do you have any opinions about choosing the symmetric or antisymmetric channel first? Do we know if there are any conventions around this, or can we really just pick freely?
If so, I'd be happy to merge and tag this!
| Base.hash(a::A4Irrep, h::UInt) = hash(a.n, h) | ||
| Base.convert(::Type{A4Irrep}, n::Integer) = A4Irrep(n) | ||
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| Base.getindex(::IrrepTable, ::Type{A₄}) = A4Irrep |
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Note that here you could in principle also register the lower order alternating group versions, something like
Base.getindex(::IrrepTable, ::Type{Alternating{3}}) = ZNIrrep{3}though that might be more confusing than helpful?
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Even though I started with including the lower degree groups, and whether or not it's confusing or helpful, I don't think that making these identifications is particularly useful.
I don't know if there is any convention. I am actually not really familiar with the representation theory of A4. So I don't have strong opinions. Is this something @lalooten knows more about? |
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Had a quick chat with @lalooten, seems like there isn't really any convention to keep in mind, so I will merge and release this as it is now. Thanks again @borisdevos ! |
This PR adds the representations of A_N for 0 < N < 5. In particular, RepA4 has a generic fusion style, which is currently untested in TensorKit.This PR adds the representations of the alternating group of degree 4, providing a sector with generic fusion style.
Credits to @lkdvos for several parts of this PR.