Representation theory of type B and C standard Levi W-algebras

TL;DR

This paper classifies finite-dimensional irreducible representations of finite W-algebras associated with standard Levi nilpotent orbits in classical Lie algebras of types B and C, using highest weight theory.

Contribution

It provides an explicit classification of these representations in terms of highest weight theory, extending understanding in types B and C.

Findings

Explicit classification of representations for type B and C W-algebras

Use of highest weight theory for classification

Connection to standard Levi nilpotent orbits

Abstract

We classify the finite dimensional irreducible representations with integral central character of finite $W$-algebras $U(\mathfrak g,e)$ associated to standard Levi nilpotent orbits in classical Lie algebras of types B and C. This classification is given explicitly in terms of the highest weight theory for finite $W$-algebras.