Dissertation/Thesis Abstract

An explicit construction of the character table for Aut( S6): Representations of Aut(S6)
by Sutton, Jared R., M.S., California State University, Long Beach, 2016, 90; 10240421
Abstract (Summary)

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.

Indexing (document details)
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
Subjects: Mathematics
Keywords: Automorphism, Character, Module, Representation, Symmetric group, Tableau
Publication Number: 10240421
ISBN: 978-1-369-39366-8
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