Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
LieART`
DecomposeProduct |
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Details and Options
Examples
(6)
Basic Examples
(4)
Decompose the tensor product ⊗8 of SU(3):
3
In[1]:=
DecomposeProduct[Irrep[SU3][8],Irrep[SU3][8]]
Out[1]=
1+2(8)+10++27
10
In[2]:=
%//InputForm
Out[2]//InputForm=
IrrepPlus[Irrep[A][0, 0], IrrepTimes[2, Irrep[A][1, 1]], Irrep[A][3, 0], Irrep[A][0, 3], Irrep[A][2, 2]]
Decompose more than two irreps, e.g. of SU(5):
10⊗10⊗5
In[1]:=
DecomposeProduct[Irrep[SU5][10],Irrep[SU5][10],Irrep[SU5][5]]
Out[1]=
1+2(24)+2(75)+126+
′
175
Decomposition of of :
27⊗
27
E
6
In[1]:=
DecomposeProduct[Irrep[E6][27],Irrep[E6][Bar[27]]]
Out[1]=
1+78+650
Displaying the results with Dynkin labels:
In[2]:=
%//StandardForm
Out[2]//StandardForm=
(000000)+(000001)+(100010)
Decomposition of irreps of product algebras, e.g. for SU(3)⊗SU(2): the decomposition of :
(,)⊗(3,1)⊗(1,2)
3
2
In[1]:=
DecomposeProduct[ProductIrrep[Irrep[SU3][Bar[3]],Irrep[SU2][2]],ProductIrrep[Irrep[SU3][3],Irrep[SU2][1]],ProductIrrep[Irrep[SU3][1],Irrep[SU2][2]]]
Out[1]=
(1,1)+(1,3)+(8,1)+(8,3)
Yukawa Interaction in
(1)
Yukawa Interaction in Minimal Flavor Violation
(1)
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