Representation theory of type B and C standard Levi W-algebras
  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. 
Jonathan Brown, Simon M. Goodwin
math.RT