2025/01/08 by Naoki Genra, Genra, Naoki, Thibault Juillard +1 · 2 citations
Computer Science · #Advanced Algebra and Logic #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Formal Methods in Verification #Logic, programming, and type systems #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2501.04501
openalex publication_date 2025/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a pair of nilpotent orbits in a simple Lie algebra, one can associate a pair of vertex algebras called affine W-algebras. Under some compatibility conditions on these orbits, we prove that one of these W-algebras can be obtained as the quantum Hamiltonian reduction of the other. This property is called reduction by stages. We provide several examples in classical and exceptional types. To prove reduction by stages for affine W-algebras, we use our previous work on reduction by stages for the Slodowy slices associated with these nilpotent orbits, these slices being the associated varieties of the W-algebras. We also prove and use the fact that each W-algebra can be defined using several equivalent BRST cohomology constructions: choosing the right BRST complexes allows us to connect the two W-algebras in a natural way.