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Explore the fascinating world of affine W-algebras in this 55-minute lecture by Jethro Van Ekeren, part of the Workshop on Quantum symmetries at the Centre de recherches mathématiques (CRM). Delve into the construction of these interesting vertex algebras through quantum Hamiltonian reduction, and gain a comprehensive understanding of their basic theory. Get a rapid introduction to vertex algebras, though some prior familiarity is beneficial. Examine Virasoro minimal models and their generalizations, obtained through Hamiltonian reduction of admissible modules of affine Lie algebras. Conclude with insights from joint work with T. Arakawa on tensor categories of representations of W-algebras. This lecture is part of a series on Affine W-algebras, offering a self-contained account of these complex mathematical structures.
