Wolfram Language
Paclet Repository
Community-contributed installable additions to the Wolfram Language
Primary Navigation
Categories
Cloud & Deployment
Core Language & Structure
Data Manipulation & Analysis
Engineering Data & Computation
External Interfaces & Connections
Financial Data & Computation
Geographic Data & Computation
Geometry
Graphs & Networks
Higher Mathematical Computation
Images
Knowledge Representation & Natural Language
Machine Learning
Notebook Documents & Presentation
Scientific and Medical Data & Computation
Social, Cultural & Linguistic Data
Strings & Text
Symbolic & Numeric Computation
System Operation & Setup
Time-Related Computation
User Interface Construction
Visualization & Graphics
Random Paclet
Alphabetical List
Using Paclets
Create a Paclet
Get Started
Download Definition Notebook
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`
P
r
o
d
u
c
t
A
l
g
e
b
r
a
P
r
o
d
u
c
t
A
l
g
e
b
r
a
[
a
l
g
e
b
r
a
s
]
g
a
t
h
e
r
s
s
i
m
p
l
e
L
i
e
a
l
g
e
b
r
a
s
t
o
a
p
r
o
d
u
c
t
a
l
g
e
b
r
a
.
Examples
(
1
)
Basic Examples
(
1
)
Entering the product algebra corresponding to the Standard-Model gauge group:
I
n
[
1
]
:
=
P
r
o
d
u
c
t
A
l
g
e
b
r
a
[
S
U
3
,
S
U
2
,
U
1
]
O
u
t
[
1
]
=
S
U
(
3
)
×
S
U
(
2
)
×
U
(
1
)
ProductAlgebra is mostly used to specify the semi-simple or non-semisimple subalgebra in subalgebra decompositions:
I
n
[
2
]
:
=
D
e
c
o
m
p
o
s
e
I
r
r
e
p
[
I
r
r
e
p
[
S
U
5
]
[
1
0
]
,
P
r
o
d
u
c
t
A
l
g
e
b
r
a
[
S
U
3
,
S
U
2
,
U
1
]
]
O
u
t
[
2
]
=
(
1
,
1
)
(
-
6
)
+
(
3
,
1
)
(
4
)
+
(
3
,
2
)
(
-
1
)
S
e
e
A
l
s
o
A
l
g
e
b
r
a
R
e
l
a
t
e
d
G
u
i
d
e
s
▪
L
i
e
A
R
T
:
L
i
e
A
l
g
e
b
r
a
s
a
n
d
R
e
p
r
e
s
e
n
t
a
t
i
o
n
T
h
e
o
r
y
"
"