Generalized Finite and Affine W-Algebras from Nilpotent Centralizers in Type A
A two-parameter family of W-algebras indexed by a pair of partitions (lambda, mu): lambda fixes a nilpotent element and its centralizer in gl_N, while mu fixes a grading on that centralizer. The affine members are built as BRST cohomology of a quantum Drinfeld-Sokolov complex and the finite members are recovered by the Zhu functor, giving a single construction that specializes to the Kac-Roan-Wakimoto W-algebras, universal affine vertex algebras of centralizers, and other previously separate objects.
2501.00271
This paper constructs a two-parameter family of affine W-algebras W^k(lambda, mu), indexed by a partition lambda (which fixes a nilpotent element and its centralizer a in gl_N) and a partition mu (wh…