MATH 5220: Introduction to Representation Theory

Description: Introduction to the representation theory of finite groups and Lie algebras. Characters, induced representations, representations of the symmetric and general linear groups, symmetric functions, Schur-Weyl duality, representations of complex semi-simple Lie algebras, and the Weyl character formulae.

Prerequisites: MATH 5210.

Credits: 3

MATH 5220 - Section 1: Introduction to Representation Theory

Description: This course is an introduction to quivers and their representations with a focus on applications to the representation theory of finite dimensional algebras over a field. A quiver is a set of points and a set of arrows between the points, and a representations of a quiver consist of one vector space for each point and one linear map for each arrow. These representations can be thought of modules over a corresponding finite dimensional algebra defined in terms of paths in the quiver. Topics covered in the course include: representations of quivers, direct sums, morphisms, kernels, exact sequences, projective and injective representations, Auslander-Reiten quiver, algebras, modules, idempotents, path algebras, Auslander-Reiten theory. We will use the language of category theory throughout the course.

Prerequisites: MATH 5210.

Offered: Fall

Credits: 0