Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Wolfram`TensorNetworks`Symmetry`
YoungSymmetrize  |
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Details and Options
Examples
(7)
Basic Examples
(1)
Symmetrize a rank-2 tensor over the row of the totally symmetric tableau {2}; the result is the unnormalized symmetric part t+:
T
t
In[1]:=
YoungSymmetrize[{{1,2},{3,4}},YoungTableau[{2}]]
Out[1]=
{{2,5},{5,8}}
Antisymmetrize over the column of the totally antisymmetric tableau {1,1}; the result is the unnormalized antisymmetric part t-:
T
t
In[2]:=
YoungSymmetrize[{{1,2},{3,4}},YoungTableau[{1,1}]]
Out[2]=
{{0,-1},{1,0}}
Apply the mixed-symmetry projector of shape {2,1} to a rank-3 symbolic array:
In[3]:=
YoungSymmetrize[Array[a,{2,2,2}],YoungTableau[{2,1}]]
Out[3]=
{{{0,2a[1,1,2]-a[1,2,1]-a[2,1,1]},{0,a[1,2,2]+a[2,1,2]-2a[2,2,1]}},{{-2a[1,1,2]+a[1,2,1]+a[2,1,1],0},{-a[1,2,2]-a[2,1,2]+2a[2,2,1],0}}}
Scope
(4)
Applications
(1)
Properties & Relations
(1)
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