Subsections
- Introduction to multilinear algebra, tensor algebra, symmetric
algebra and exterior algebra.
- Representations and basic examples, direct sum and tensor product
of representations.
- Irreducible representations, complete reducibility and
Maschke's theorem, Schur's lemma.
- Character theory of representations, orthogonality relations,
decomposition of the regular representation.
- Character tables of Abelian, dihedral and small groups.
- Dimension theorem, Burnside's
-theorem.
- Restriction of a representation, induced representations,
Frobenius reciprocity, Mackey's irreducibility criterion.
- Representation theory of symmetric groups.
- Benjamin Steinberg, Representation Theory of Finite
Groups, Springer (Universitext), 2012.
- Gordon James and Martin Liebeck, Representations and Characters of
Groups, Cambridge University Press, 2001.
- William Fulton and Joe Harris, Representation Theory: A First
Course, Springer (Graduate Texts in Mathematics 129), 1991.
- Jean-Pierre Serre, Linear Representations of Finite
Groups, Springer (Graduate Texts in Mathematics 42), 1977.
