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Learn More about
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`
L
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Examples
(
5
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Basic Examples
(
4
)
L
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X
F
o
r
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of single irreps:
I
n
[
1
]
:
=
I
r
r
e
p
[
S
U
5
]
[
5
]
/
/
L
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X
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O
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t
[
1
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/
/
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=
\
i
r
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p
{
5
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I
n
[
2
]
:
=
I
r
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p
[
S
U
5
]
[
B
a
r
[
5
]
]
/
/
L
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X
F
o
r
m
O
u
t
[
2
]
/
/
L
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X
F
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m
=
\
i
r
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p
b
a
r
{
5
}
Product algebra irreps in
L
a
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X
F
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:
I
n
[
1
]
:
=
P
r
o
d
u
c
t
I
r
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p
[
I
r
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p
[
S
U
3
]
[
B
a
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[
3
]
]
,
I
r
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p
[
S
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2
]
[
1
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,
I
r
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p
[
U
]
[
-
2
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]
O
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t
[
1
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=
(
3
,
1
)
(
-
2
)
I
n
[
2
]
:
=
%
/
/
L
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O
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[
2
]
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/
L
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F
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=
(
\
i
r
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p
b
a
r
{
3
}
,
\
i
r
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p
{
1
}
)
(
-
2
)
Results of tensor product decompositions in
L
a
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X
F
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:
I
n
[
1
]
:
=
D
e
c
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p
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P
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d
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[
I
r
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p
[
S
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3
]
[
8
]
,
I
r
r
e
p
[
S
U
3
]
[
8
]
]
O
u
t
[
1
]
=
1
+
2
(
8
)
+
1
0
+
1
0
+
2
7
I
n
[
2
]
:
=
%
/
/
L
a
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X
F
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O
u
t
[
2
]
/
/
L
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X
F
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=
$
\
i
r
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p
{
1
}
+
2
(
\
i
r
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p
{
8
}
)
+
\
i
r
r
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p
{
1
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+
\
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p
b
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{
1
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}
+
\
i
r
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p
{
2
7
}
$
L
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E
X
output of decompositions to subalgebras:
I
n
[
1
]
:
=
D
e
c
o
m
p
o
s
e
I
r
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p
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[
2
4
]
,
P
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A
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,
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1
]
]
O
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[
1
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=
(
1
,
1
)
(
0
)
+
(
1
,
3
)
(
0
)
+
(
3
,
2
)
(
5
)
+
(
3
,
2
)
(
-
5
)
+
(
8
,
1
)
(
0
)
I
n
[
2
]
:
=
%
/
/
L
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F
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[
2
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=
$
(
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r
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p
{
1
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,
\
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{
1
}
)
(
0
)
+
(
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r
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p
{
1
}
,
\
i
r
r
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p
{
3
}
)
(
0
)
+
(
\
i
r
r
e
p
{
3
}
,
\
i
r
r
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p
{
2
}
)
(
5
)
+
(
\
i
r
r
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p
b
a
r
{
3
}
,
\
i
r
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p
{
2
}
)
(
-
5
)
+
(
\
i
r
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p
{
8
}
,
\
i
r
r
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p
{
1
}
)
(
0
)
$
A
p
p
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c
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(
1
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▪
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