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 sln orbital varieties are described by Young tableaux. In this paper we consider so-called Richardson orbital varieties in sln. A Richardson orbital variety is an orbital variety whose closure is a standard nilradical. We show that in sln 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 sln in terms of Young tableaux.
ASJC Scopus subject areas
- Algebra and Number Theory