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Wolfram Language
LieART
Guides
LieART: Lie Algebras and Representation Theory
Tech Notes
LieART - Quick Start Tutorial
Symbols
Algebra
CartanMatrix
DecomposeIrrep
DecomposeProduct
DimName
Dim
HighestRoot
Index
Irrep
IrrepPlus
LaTeXForm
MetricTensor
OrthogonalSimpleRoots
PositiveRoots
ProductAlgebra
ProductIrrep
RootSystem
WeightSystem
YoungTableau
Other
BranchingRules
IrrepProperties
TensorProducts
LieART`
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Examples
(
3
)
Basic Examples
(
2
)
Young tableau of the fundamental representation of SU(3):
I
n
[
1
]
:
=
Y
o
u
n
g
T
a
b
l
e
a
u
[
I
r
r
e
p
[
S
U
3
]
[
3
]
]
O
u
t
[
1
]
=
Young tableau of the
8
of SU(3):
I
n
[
2
]
:
=
Y
o
u
n
g
T
a
b
l
e
a
u
[
I
r
r
e
p
[
S
U
3
]
[
8
]
]
O
u
t
[
2
]
=
Young tableau of the
27
of SU(3):
I
n
[
3
]
:
=
Y
o
u
n
g
T
a
b
l
e
a
u
[
I
r
r
e
p
[
S
U
3
]
[
2
7
]
]
O
u
t
[
3
]
=
Young tableau of the
720
of SU(5):
I
n
[
1
]
:
=
Y
o
u
n
g
T
a
b
l
e
a
u
[
I
r
r
e
p
[
A
]
[
1
,
2
,
0
,
1
]
]
O
u
t
[
1
]
=
Young tableau of the of the SU(5) singlet:
I
n
[
2
]
:
=
Y
o
u
n
g
T
a
b
l
e
a
u
[
I
r
r
e
p
[
A
]
[
0
,
0
,
0
,
0
]
]
O
u
t
[
2
]
=
A
p
p
l
i
c
a
t
i
o
n
s
(
1
)
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▪
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