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Linear representation theory of symmetric group:S3

86 bytes added, 15:48, 27 May 2011
Interpretation as symmetric group
{| class="sortable" border="1"
! Common name of representation !! Degree !! Corresponding [[Unordered integer partition|partition]] corresponding to representation !! Young diagram !! [[Hook-length formula]] for degree !! Quick rule for character computation
|-
| [[trivial representation]] || 1 || 3 || [[File:Youngdiag3.png]] || <math>\frac{3!}{3 \cdot 2 \cdot 1}</math> || 1 everywhere
|-
| [[sign representation]] || 1 || 1 + 1 + 1 || [[File:Youngdiag1-1-1.png]] || <math>\frac{3!}{3 \cdot 2 \cdot 1}</math> || 1 for even, -1 for odd
|-
| [[standard representation]] || 2 || 2 + 1 || [[File:Youngdiag2-1.png]] || <math>\frac{3!}{3 \cdot 1 \cdot 1}</math> || (number of fixed points of permutation) - 1
|}
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