MATH8246: Representation Theory

Basics of characters of groups include: Finite groups and Maschke theorem; Characters of finite groups and their orthogonality; character tables; Virtual and induced characters; Frobenius formula and Frobenius reciprocity. Basics of specializations to symmetric groups include: Specht modules; Schur-Weyl duality; and representations of general linear groups over the field of complex numbers. Basics of representations of algebras include: Tensor products; Indecomposable representations and semisimple algebras; Jordan-Holder and Krull-Schmidt theorems. Basics of quiver representations include: Path algebras; Indecomposable representations of Dynkin quivers; Gabriel's theorem; Reflection functors; Projective and injective modules; Tor and Ext; Projective covers. This is a first-year graduate course and has its prerequisites: Math 5285H and Math 5286H.

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