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- Title
Universal filtered quantizations of nilpotent Slodowy slices.
- Authors
Ambrosio, Filippo; Carnovale, Giovanna; Esposito, Francesco; Topley, Lewis
- Abstract
Every conic symplectic singularity admits a universal Poisson deformation and a universal filtered quantization, thanks to the work of Losev and Namikawa. We begin this paper by showing that every such variety admits a universal equivariant Poisson deformation and a universal equivariant quantization with respect to a reductive group acting on it by C*-equivariant Poisson automorphisms. We go on to study these definitions in the context of nilpotent Slodowy slices. First, we give a complete description of the cases in which the finite W -algebra is a universal filtered quantization of the slice, building on the work of Lehn--Namikawa--Sorger. This leads to a near-complete classification of the filtered quantizations of nilpotent Slodowy slices. The subregular slices in non-simply laced Lie algebras are especially interesting: with some minor restrictions on Dynkin type, we prove that the finite W -algebra is a universal equivariant quantization with respect to the Dynkin automorphisms coming from the unfolding of the Dynkin diagram. This can be seen as a non-commutative analogue of Slodowy's theorem. Finally, we apply this result to give a presentation of the subregular finiteW -algebra of type B as a quotient of a shifted Yangian.
- Subjects
DYNKIN diagrams; LIE algebras; NILPOTENT Lie groups; GEOMETRIC quantization
- Publication
Journal of Noncommutative Geometry, 2024, Vol 18, Issue 1, p1
- ISSN
1661-6952
- Publication type
Article
- DOI
10.4171/JNCG/544