Mathematics: Representation Theory

<p>The course gives an introduction to representations of finite groups over the complex numbers and to character theory.</p><p>The course treats:</p> <ul> <li>Group representations: linear representations, equivalent representations, regular representation, induced and restricted representations, irreducible representations, Maschke’s Theorem, dual representations and tensor product of representations.</li> <li>Character theory: characters of representations, induced characters, irreducible characters, orthogonality relations, integrality, character tables, the Mackey formula, Frobenius reciprocity.</li> <li>Applications to groups: Burnside’s Theorem, Frobenius’ Theorem, Frobenius divisibility.</li> </ul>