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

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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.

Original languageEnglish
JournalInventiones Mathematicae
Early online date21 Aug 2023
DOIs
Publication statusE-pub ahead of print - 21 Aug 2023

Bibliographical note

Funding Information:
This research is supported by the UKRI Future Leaders Fellowship project “Geometric representation theory and -algebras”, grant numbers MR/S032657/1, MR/S032657/2, MR/S032657/3.

Publisher Copyright:
© 2023, The Author(s).

ASJC Scopus subject areas

  • Mathematics(all)

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