All Questions
Tagged with young-tableaux lie-algebras
12
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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
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34
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Constructing Young tableaux basic question
I'm trying to understand Young tableaux and was making some exercises.
I'm a bit confused with the following question
Given a tensor $B^{ijk}$ where $B^{ijk} = -B^{jik}$ and $B^{ijk} + B^{kij} + B^{...
- 796
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Embed U(5) to U(16) by specifying the 16-dimensional complex representation
$\DeclareMathOperator\SU{SU}\DeclareMathOperator\U{U}\DeclareMathOperator\Spin{Spin}$
My question concerns all the possible ways to embed SU(5) to U(16) by specifying the 16-dimensional complex ...
- 5,969
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Creation-Annihilation operators and Young diagrams
Let assume a Fock space written as,
$$F=\bigoplus_\rho V_\rho,$$
where $V_\rho$ is an irreducible representation of $U(N)$ labeled by a partition (Young diagram) $\rho$. For the so-called bosonic case ...
3
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1
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Explicit construction of a representation of Young diagram/tableaux from fundamental representations
Given $SU(N)$ fundamental representation say $U^i$ in the fundamental $N$ of $SU(N)$, with indices $i=1,2,3,\dots,N$.
We can construct a representation whose Young diagram/tableaux look like
Given
...
- 3,697
3
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0
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253
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Complex conjugated representation and Young tableaux
Imagine you have the Young tableu and the Dynkin numbers, $(q_1, q_2, ..., q_r)$, of the Lie algebra of $SU(n)$ which has $r$ simple roots. The way I assign Dynkin numbers is increasing its value from ...
- 549
4
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What is the mistake in finding the irreps of $SU(3)$ multiplets $6 \otimes 8$, or $15 \otimes \bar{15}$?
I wrote a Mathematica paclet that can be used to find irreducible representations of $SU(n)$.
Specifically, given a product of $SU(n)$ multiplets, it can compute the corresponding sum.
To test the ...
- 153
1
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1
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Young Diagrams, singlets and ignoring the first column
Consider the following Young diagram of $SU(5)$
Now from what I have learned we can ignore the first column of this (since it has 5 elements) and thus write it as:
Now if we write down the tensor ...
1
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1
answer
830
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Young Tableaux of $SU(N)$: Group or Algebra?
I am slightly confused about the use of Young Tableaux in the context of the Lie group and Lie algebras of $SU(N)$. A Young Tableaux has an associated representation which acts on a tensor e.g. $\psi_{...
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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 $...
1
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1
answer
71
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Basis of the representations of the B and C series Lie groups
As is well-known, the representations of $SU(n)$ are labelled by Young diagrams. Moreover, there exists a canonical basis of each representation labelled by all the possible tableaux of the diagram.
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2
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1
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96
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Tensoring Young Tableaus
As we all know very well, the finite dimensional irreducible representations of the compact Lie groups $SU(N)$ are labelled by Young tableaus. Now when we tensor two irreducible representations we get ...
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