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Community-contributed installable additions to the Wolfram Language
Wolfram`TensorNetworks`Symmetry`
TableauDimension  |
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Details and Options
Examples
(6)
Scope
(4)
From tableau vs partition
(1)
When the argument is a Young tableau the shape is read off and the dimension depends only on that shape; the explicit standard tableau {{1,2},{3}} has shape {2,1}, so the irrep dimension is 2:
In[1]:=
TableauDimension[YoungTableau[{{1,2},{3}}]]
Out[1]=
2
A single-row tableau corresponds to the fully symmetric (trivial) irrep, which is one-dimensional:
In[1]:=
TableauDimension[YoungTableau[{{1,2,3}}]]
Out[1]=
1
A single-column tableau corresponds to the fully antisymmetric (sign) irrep, also one-dimensional:
In[1]:=
TableauDimension[YoungTableau[{{1},{2},{3}}]]
Out[1]=
1
Passing the bare partition gives the same result; no filling of boxes is needed:
In[1]:=
TableauDimension[{2,1}]
Out[1]=
2
Hook-length formula
(1)
Symmetric, antisymmetric, and mixed
(1)
Sum-of-squares identity
(1)
Applications
(1)
Properties & Relations
(1)
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Dimension of the irrep of corresponding to a Young tableau of shape {3,2}:
S
5
In[1]:=
TableauDimension[YoungTableau[{3,2}]]
Out[1]=
5
Equivalently, called directly on the partition:
In[2]:=
TableauDimension[{3,2}]
Out[2]=
5
The fully symmetric and fully antisymmetric irreps are one-dimensional:
In[3]:=
{TableauDimension[{4}],TableauDimension[{1,1,1,1}]}
Out[3]=
{1,1}
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