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

Jonathan Brown and Simon M. Goodwin

Vol. 269 (2014), No. 1, 31–71

DOI: 10.2140/pjm.2014.269.31

Abstract

We classify the finite-dimensional irreducible representations with integral central character of finite $W$-algebras $U\left(\mathfrak{g},e\right)$ 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.

Keywords

$W$-algebras, representation theory

Mathematical Subject Classification 2010

Primary: 17B10, 81R05

Milestones

Received: 22 November 2012

Revised: 15 October 2013

Accepted: 31 October 2013

Published: 15 July 2014