Affine W-algebras - Part I

Explore the fascinating world of affine W-algebras in this comprehensive lecture from the Workshop on Quantum symmetries at the Centre de recherches mathématiques. Delve into the construction of these intriguing vertex algebras through quantum Hamiltonian reduction, and gain a solid understanding of their fundamental theory. Begin with a quick introduction to vertex algebras, though some prior knowledge in this area is beneficial. Examine Virasoro minimal models and their generalizations, obtained through Hamiltonian reduction of admissible modules of affine Lie algebras. Conclude by discovering the results of collaborative research with T. Arakawa on tensor categories of W-algebra representations. This in-depth, hour-long presentation is ideal for mathematicians and physicists interested in quantum symmetries, tensor categories, and topological quantum field theories.