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Linear representation theory of symmetric group:S3

No change in size, 00:28, 30 July 2011
Induced representations from subgroups
| 3-Sylow subgroup, i.e., the alternating group <math>\{ (), (1,2,3), (1,3,2) \}</math> || trivial representation || takes the value <math>2</math> on even permutations and <math>0</math> on odd permutations || trivial representation and sign representation
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| 3-Sylow subgroup, i.e., the alternating group <math>\{ (), (1,2,3), (1,3,2) \}</math> || nontrivial representation || takes the value <math>12</math> at the identity element, <math>-1</math> at 3-cycles, and <matH>0</math> outside || standard representation
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| 2-Sylow subgroup, such as <math>\{ (), (1,2) \}</math> || trivial representation || takes the value 3 at the identity element, 1 at each 2-transposition, and 0 at the 3-cycles || trivial representation and standard representation
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