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Project.toc
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\boolfalse {citerequest}\boolfalse {citetracker}\boolfalse {pagetracker}\boolfalse {backtracker}\relax
\babel@toc {english}{}
\defcounter {refsection}{0}\relax
\contentsline {section}{\numberline {1}Introduction}{1}{section.1}%
\defcounter {refsection}{0}\relax
\contentsline {subsection}{\numberline {1.1}Overview of Project}{1}{subsection.1.1}%
\defcounter {refsection}{0}\relax
\contentsline {subsection}{\numberline {1.2}An Overview of the History of Representation Theory}{1}{subsection.1.2}%
\defcounter {refsection}{0}\relax
\contentsline {section}{\numberline {2}Representation Theory}{3}{section.2}%
\defcounter {refsection}{0}\relax
\contentsline {subsection}{\numberline {2.1}Group Representations}{3}{subsection.2.1}%
\defcounter {refsection}{0}\relax
\contentsline {subsection}{\numberline {2.2}Representation Reducibility}{8}{subsection.2.2}%
\defcounter {refsection}{0}\relax
\contentsline {section}{\numberline {3}$FG$-Modules}{14}{section.3}%
\defcounter {refsection}{0}\relax
\contentsline {subsection}{\numberline {3.1}Basic Definitions}{14}{subsection.3.1}%
\defcounter {refsection}{0}\relax
\contentsline {subsection}{\numberline {3.2}Maschke's Theorem}{19}{subsection.3.2}%
\defcounter {refsection}{0}\relax
\contentsline {subsection}{\numberline {3.3}Schur's Lemma}{24}{subsection.3.3}%
\defcounter {refsection}{0}\relax
\contentsline {section}{\numberline {4}Character Theory}{27}{section.4}%
\defcounter {refsection}{0}\relax
\contentsline {subsection}{\numberline {4.1}Basic Definitions and Results}{27}{subsection.4.1}%
\defcounter {refsection}{0}\relax
\contentsline {subsection}{\numberline {4.2}Inner Products on Characters}{33}{subsection.4.2}%
\defcounter {refsection}{0}\relax
\contentsline {section}{\numberline {5}Character Tables}{41}{section.5}%
\defcounter {refsection}{0}\relax
\contentsline {subsection}{\numberline {5.1}Basic Definitions}{41}{subsection.5.1}%
\defcounter {refsection}{0}\relax
\contentsline {subsection}{\numberline {5.2}Orthogonality Relations}{43}{subsection.5.2}%
\defcounter {refsection}{0}\relax
\contentsline {subsection}{\numberline {5.3}Lifting Characters}{45}{subsection.5.3}%
\defcounter {refsection}{0}\relax
\contentsline {subsection}{\numberline {5.4}Linear Characters}{48}{subsection.5.4}%
\defcounter {refsection}{0}\relax
\contentsline {subsection}{\numberline {5.5}Further Examples}{53}{subsection.5.5}%
\defcounter {refsection}{0}\relax
\contentsline {section}{\numberline {6}Conclusion}{57}{section.6}%
\defcounter {refsection}{0}\relax
\contentsline {section}{\numberline {7}References}{58}{section.7}%