One dimensional representations of finite W-algebras, Dirac reduction and the orbit method

• 成果类型: Article
• 署名作者: Topley, Lewis
• 署名单位: University of Bath
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-023-01215-3
• 发表日期: 2023
• 页码: 1039-1107
• 关键词: poisson deformations; enveloping-algebras; primitive-ideals; shifted yangians; VARIETIES; slices

摘要

In this paper we study the variety of one dimensional representations of a finite W algebra attached to a classical Lie algebra, giving a precise description of the dimensions of the irreducible components. We apply this to prove a conjecture of Losev describing the image of his orbit method map. In order to do so we first establish new Yangian-type presentations of semiclassical limits of the W-algebras attached to distinguished nilpotent elements in classical Lie algebras, using Dirac reduction.