Affine W-algebras

Affine W-algebras may be considered as a generalization of infinite dimensional Lie algebras such as Kac-Moody algebras and the Virasoro algebra. They may be also regarded as an affinization of finite W-algebras, but affine W-algebras are introduced earlier than finite W-algebras in physics literature. Affine W-algebras are related with conformal field theories, integrable systems, quantum groups, the geometric Langlands program, and 4 dimensional gauge theories. In my talk I will discuss about their structure and describe their representation theory by focusing on type A cases.