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Standard representation of the symmetric group
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Permutation representation
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Words: 30
The permutation representation of
S
n
on
C
n
decomposes as
C
(
1
,
…
,
1
)
⊕
{(
x
1
,
…
,
x
n
)
:
x
1
+
⋯
+
x
n
=
0
}
.
(73)
The first summand is the trivial representation and the second is the
(
n
−
1
)
-dimensional standard representation.
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(6)
Permutation representation
Representation theory
Algebra
Area of mathematics
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