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Explore the intricacies of affine W-algebras in this 45-minute lecture from the Workshop on Quantum symmetries at the Centre de recherches mathématiques. Delve into the construction of these fascinating vertex algebras through quantum Hamiltonian reduction, and gain a comprehensive understanding of their basic theory. Receive a concise introduction to vertex algebras, though prior familiarity is beneficial. Examine Virasoro minimal models and their generalizations, derived from Hamiltonian reduction of admissible modules of affine Lie algebras. Conclude with insights into tensor categories of W-algebra representations, based on joint work with T. Arakawa. This advanced mathematical lecture is part of a series on affine W-algebras, offering a deep dive into quantum symmetries and their applications in theoretical physics and mathematics.
