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Unformatted text preview: Math 220C May 19, 2008 Some character tables (revised) In class, we have computed several character tables. (1) Character table for S 3 . 1 (12) (123)  K  1 3 2 trivial 1 1 1 det 1 1 1 V 2 1 (2) Character table for BD 4 . 1 1 ± x ± y ± xy  K  1 1 2 2 2 trivial 1 1 1 1 1 2D 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 (3) Character table for BD 6 . 1 1 x ± 1 x ± 2 y , x ± 2 y y , x ± 1 y  K  1 1 2 2 3 3 trivial 1 1 1 1 1 1 2D 2 2 1 1 1 1 1 1 i i 1 1 1 1 i i 1 1 1 1 1 1 2 2 1 1 The final row was inferred from the earlier rows. (4) Character table for S 4 . 1 (12) (123) (1234) (12)(34)  K  1 6 8 6 3 trivial 1 1 1 1 1 det 1 1 1 1 1 V 3 1 1 1 V 3 1 1 1 U 2 1 2 Here, V = V ⊗ det, and as above, the final row can be inferred from earlier rows. 1 2 (5) Character table for A 4 . We start by restricting the characters from S 4 to the subgroup A 4 , omitting duplicates....
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 Spring '08
 MORRISON
 Math, Algebra, Group Theory, character table

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