Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Wolfram`TensorNetworks`Symmetry`
HookFactor  |
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Details and Options
Examples
(6)
Scope
(4)
Partition vs tableau
(1)
The bare partition and any Young tableau of that shape give the same factor:
In[1]:=
HookFactor[{4,2,1}]
Out[1]=
1
144
A standard tableau on {4,2,1} reads its shape and returns the same value:
In[1]:=
HookFactor[YoungTableau[{{1,2,3,4},{5,6},{7}}]]
Out[1]=
1
144
Two distinct standard fillings of {3,2} produce the same factor, since only the shape matters:
In[1]:=
{HookFactor[YoungTableau[{{1,2,3},{4,5}}]],HookFactor[YoungTableau[{{1,3,5},{2,4}}]]}
Out[1]=
,
1
24
1
24
Dimension identity
(1)
Symmetric and antisymmetric extremes
(1)
Frobenius vs hook-product
(1)
Applications
(1)
Properties & Relations
(1)
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HookFactor for the partition {2, 1}:
In[1]:=
HookFactor[{2,1}]
Out[1]=
1
3
A larger partition is just as cheap:
In[2]:=
HookFactor[{3,2}]
Out[2]=
1
24
From a Young tableau, only its shape is read:
In[3]:=
HookFactor[YoungTableau[{3,2}]]
Out[3]=
1
24
Multiplied by n! gives the irrep dimension, recovering TableauDimension:
In[4]:=
5!*HookFactor[{3,2}]
Out[4]=
5
""