Academic Journal
Universal filtered quantizations of nilpotent Slodowy slices
| العنوان: | Universal filtered quantizations of nilpotent Slodowy slices |
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| المؤلفون: | Ambrosio, Filippo, Carnovale, Gioavanna, Esposito, Francesco, Topley, Lewis |
| المصدر: | Ambrosio , F , Carnovale , G , Esposito , F & Topley , L 2024 , ' Universal filtered quantizations of nilpotent Slodowy slices ' , Journal of Noncommutative Geometry , vol. 18 , no. 1 , pp. 1-35 . https://doi.org/10.4171/jncg/544 |
| سنة النشر: | 2024 |
| مصطلحات موضوعية: | Poisson deformations, Slodowy slices, W -algebras, filtered quantizations, /dk/atira/pure/subjectarea/asjc/2600/2602, name=Algebra and Number Theory, /dk/atira/pure/subjectarea/asjc/2600/2610, name=Mathematical Physics, /dk/atira/pure/subjectarea/asjc/2600/2608, name=Geometry and Topology |
| الوصف: | 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 X -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 finite W -algebra of type B as a quotient of a shifted Yangian. |
| نوع الوثيقة: | article in journal/newspaper |
| وصف الملف: | application/pdf |
| اللغة: | English |
| DOI: | 10.4171/jncg/544 |
| الاتاحة: | https://researchportal.bath.ac.uk/en/publications/3b8f795a-3ba0-4fac-8c4d-b1ac764f5e83 https://doi.org/10.4171/jncg/544 https://purehost.bath.ac.uk/ws/files/300447149/ACET-published.pdf http://www.scopus.com/inward/record.url?scp=85185786164&partnerID=8YFLogxK |
| Rights: | info:eu-repo/semantics/openAccess |
| رقم الانضمام: | edsbas.77A8CDED |
| قاعدة البيانات: | BASE |
| DOI: | 10.4171/jncg/544 |
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