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arXiv · 2102.00903

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

Lewis Topley
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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.

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Lewis Topley. 2021-02-01. One dimensional representations of finite $W$-algebras, Dirac reduction and the orbit method. https://arxiv.org/abs/2102.00903

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