报告题目：Lectures on Quiver Representations
主 讲 人：Antoine Caradot
ZOOM ID：567 306 5241
Quivers and their representations were introduced in the second half of the last century to study problems in linear algebra, such as classifying tuples of subspaces of a prescribed vector space. They soon became quite prominent in the representation theory of finite dimensional algebras, and even beyond with connections to domains like Kac-Moody algebras or geometric invariant theory. The purpose of these lectures is to give an introduction to the representation theory of quivers and to describe one of its connections with Kac-Moody algebras. The plan is as follows: 1. The first section will present the definitions of quivers, representations, path algebras and their first properties. We will introduce the classification problem and describe the simple and indecomposable projective modules of quivers without oriented cycles. 2. In the second section we will introduce the representation space of a quiver. As it is equipped with an action of a product of general linear groups, we can describe the orbits of this action. From there, we will be able to prove the classification of quivers of finite orbit type, and we will then explain the classification of tame quivers. 3. The third section is devoted to a connection between quivers and Kac-Moody algebras. We will describe how the construction of Nakajima’s quiver varieties provides a realisation of the irreducible highest weight integrable representations of Kac-Moody algebras.
Antoine Caradot is now a postdoctor in School of Mathematics and Statistics of Henan University. His main research interest is the representation theory.