char-tables-v2

char-tables-v2 - Math 220C May 19, 2008 Some character...

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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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This note was uploaded on 08/06/2008 for the course MATH 220 taught by Professor Morrison during the Spring '08 term at UCSB.

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char-tables-v2 - Math 220C May 19, 2008 Some character...

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