The center of the symmetric group Sn is trivial for n > 2. For n ≠ 6, S n ≃Aut(Sn). When n = 6, [Aut( S6) : Inn(S6] = 2. To understand the structure of A=Aut(S6), we study its linear (group) representations over C. A linear representation will later be defined as a module over the group ring CA. Maschke's Theorem implies that every finite dimensional linear representation decomposes into a finite direct sum of irreducible representations. Our goal is to find a character table for A. The character of a group element is the trace of the corresponding matrix under the representation. A character table is an array of characters. Start with irreducible representations of S6 and invoke the Induced Character Theorem to find representations of A. Representations of A may or may not be irreducible after induction. Since conjugacy classes of S n are in one-to-one correspondence with partitions of n, there is a beautiful combinatorial theory that enables us to explicitly construct all irreducible representations of Sn.
|Advisor:||Murray, William L.|
|Commitee:||Brevik, John O., Valentini, Robert C.|
|School:||California State University, Long Beach|
|Department:||Mathematics and Statistics|
|School Location:||United States -- California|
|Source:||MAI 56/02M(E), Masters Abstracts International|
|Keywords:||Automorphism, Character, Module, Representation, Symmetric group, Tableau|
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