All Questions
Tagged with young-tableaux tensor-products
6
questions
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Dimension of irreducible totally-symmetric tensor product of two su(n) representations
Consider the irreducible representation of $\mathfrak{su}$(n) given by the Young tableu
The dimension of the representation is easily obtained by the usual rules, and it is $d=n(n-1)/2$. One can also ...
- 133
3
votes
1
answer
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Schur functors for $\mathfrak{S}_3$
I have been trying to calculate the explicit images of the Schur functors for the action of $\mathfrak{S}_3$ on $V^{\otimes 3}$ where $V$ is some vector space, for the sake of concreteness of ...
- 311
4
votes
1
answer
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Operators commuting with tensor product representations of SU(2)
I am currently investigating $SU(2)$ symmetric qubit systems. In the course of this work I proved the following theorem:
Let $S_n$ denote the permutation group of $n$ elements. For $\sigma\in S_n$ ...
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1
vote
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answer
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$8 \otimes 8$ in $SU(3)$, dimension of the Young-tableau corresponding to the $\bar{10}$
In Georgi's Lie Algebras in Particle Physics, he calculates the decomposition of $8\otimes 8$ in $SU(3)$, and obtains
$$8\otimes 8 = 27 \oplus 10 \oplus \bar{10} \oplus 8 \oplus 8 \oplus 1,$$
...
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Does $\mathbf{n}\otimes \mathbf{m}=\mathbf{m}\otimes \mathbf{n}$ in the Clebsch-Gordan decomposition?
Consider the two irreducible representations, $\mathbf{n}$ and $\mathbf{m}$, of $su_\Bbb{C}(N)$. The tensor product $\mathbf{n}\otimes \mathbf{m}$ can be found using Young tableaux as follows:
Write $...
6
votes
2
answers
992
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Littlewood Richardson rules for the orthogonal group SO(d)
I have a question related to tensor products of Young diagrams. More precisely, I know the Littlewood Richardson rules for the general linear group GL(d) and would like to know the restriction of ...
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