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- Title
One dimensional representations of finite W-algebras, Dirac reduction and the orbit method.
- Authors
Topley, Lewis
- Abstract
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.
- Subjects
SEMICLASSICAL limits; LIE algebras; ORBIT method
- Publication
Inventiones Mathematicae, 2023, Vol 234, Issue 3, p1039
- ISSN
0020-9910
- Publication type
Article
- DOI
10.1007/s00222-023-01215-3