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The finite general linear group for coefficients the prime field .
The character table for over the complex numbers looks like that of the binary octahedral group. The only difference is the Schur indices. Hence the character tables over the real numbers do differ.
linear representation theory of the finite general linear group GL(2,3)
conjugacy classes: | 1 | 2A | 2B | 3 | 4 | 6 | 8A | 8B |
---|---|---|---|---|---|---|---|---|
their cardinality: | 1 | 1 | 12 | 8 | 6 | 8 | 6 | 6 |
character table over the complex numbers
irrep | 1 | 2A | 2B | 3 | 4 | 6 | 8A | 8B |
---|---|---|---|---|---|---|---|---|
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
1 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | |
2 | 2 | 0 | -1 | 2 | -1 | 0 | 0 | |
2 | -2 | 0 | -1 | 0 | 1 | |||
2 | -2 | 0 | -1 | 0 | 1 | |||
3 | 3 | -1 | 0 | -1 | 0 | 1 | 1 | |
3 | 3 | 1 | 0 | -1 | 0 | -1 | -1 | |
4 | -4 | 0 | 1 | 0 | -1 | 0 | 0 |
character table over the rational numbers and real numbers
irrep | 1 | 2A | 2B | 3 | 4 | 6 | 8A | 8B |
---|---|---|---|---|---|---|---|---|
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
1 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | |
2 | 2 | 0 | -1 | 2 | -1 | 0 | 0 | |
4 | -4 | 0 | -2 | 0 | 2 | 0 | 0 | |
3 | 3 | -1 | 0 | -1 | 0 | 1 | 1 | |
3 | 3 | 1 | 0 | -1 | 0 | -1 | -1 | |
4 | -4 | 0 | 1 | 0 | -1 | 0 | 0 |
References
Last revised on September 2, 2021 at 08:42:27. See the history of this page for a list of all contributions to it.