Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
LieART`
Irrep  |
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Examples
(4)
Basic Examples
(3)
Enter the fundamental representation of SU(3) ( in Dynkin classification) by its Dynkin label , which is used internally to uniquely specify an irrep:
A
2
(10)
In[1]:=
Irrep[A][1,0]//FullForm
Out[1]//FullForm=
Irrep[A][1,0]
In the Dynkin label is displayed in textbook notation without separation between the digits if they are smaller than 10:
In[2]:=
Irrep[A][1,3,2,1]//StandardForm
Out[2]//StandardForm=
(1321)
and separated by commas for digits equal or larger than 10:
In[3]:=
Irrep[A][1,11,2,1]//StandardForm
Out[3]//StandardForm=
(1, 11, 2, 1)
In the dimensional name of the irrep is displayed, while computations are always using the :
In[1]:=
Irrep[A][0,0,1,0]//TraditionalForm
Out[1]//TraditionalForm=
10
The algebra class for the classical Lie algebras are A, B, C, D, while for exceptional algebras it coincides with the algebra itself, i.e. E6, E7, E8, F4 and G2. The of can be entered via its Dynkin label (000010):
27
E
6
In[2]:=
Irrep[E6][0,0,0,0,1,0]//TraditionalForm
Out[2]//TraditionalForm=
27
Alternatively irreps can be entered by their dimensional name. Instead of the algebra class one must specify the algebra itself. The input is converted to the unique form with algebra class and Dynkin label:
In[1]:=
Irrep[SU5][10]//FullForm
Out[1]//FullForm=
Irrep[A][0,1,0,0]
Conjugated irreps can be entered by applying the head Bar to the dimension:
In[2]:=
Irrep[SU5][Bar[10]]//FullForm
Out[2]//FullForm=
Irrep[A][0,0,1,0]
and irreps with a prime by the head IrrepPrime, which can be combined with Bar in any order:
In[3]:=
Irrep[SU5][IrrepPrime[Bar[175]]]
Out[3]=
′
175
Possible Issues
(1)
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