On orbital variety closures in [formula omitted]: II. Descendants of a Richardson orbital variety

Abstract

For a semisimple Lie algebra g , the orbit method attempts to assign representations of g to (coadjoint) orbits in g ∗ . Orbital varieties are particular Lagrangian subvarieties of such orbits leading to highest weight representations of g . In sl n orbital varieties are described by Young tableaux. In this paper we consider so-called Richardson orbital varieties in sl n . A Richardson orbital variety is an orbital variety whose closure is a standard nilradical. We show that in sl n a Richardson orbital variety closure is a union of orbital varieties. We give a complete combinatorial description of such closures in terms of Young tableaux. This is the second paper in the series of three papers devoted to a combinatorial description of orbital variety closures in sl n in terms of Young tableaux.