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

2021/02/01 by Topley, Lewis · 1 citation
#17B10 #17B63. Secondary 17B20 #FOS: Mathematics #Primary 17B35 #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2102.00903

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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