Generalized finite and affine W-algebras in type A

2024/12/31 by Choi, Dong Jun, Molev, Alexander, Suh, Uhi Rinn
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2501.00271

Abstract

We construct a new family of affine W-algebras W^k(λ,μ) parameterized by partitions λ and μ associated with the centralizers of nilpotent elements in \mathfrakgl_N. The new family unifies a few known classes of W-algebras. In particular, for the column-partition λ we recover the affine W-algebras W^k(\mathfrakgl_N,f) of Kac, Roan and Wakimoto, associated with nilpotent elements f∈\mathfrakgl_N of type μ. Our construction is based on a version of the BRST complex of the quantum Drinfeld-Sokolov reduction. We show that the application of the Zhu functor to the vertex algebras W^k(λ,μ) yields a family of generalized finite W-algebras U(λ,μ) which we also describe independently as associative algebras.

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