On orbital variety closures in sl(n). II. Descendants of a Richardson orbital variety

Details On orbital variety closures in sl(n). II. Descendants of a Richardson orbital variety On orbital variety closures in sl(n). II. Descendants of a Richardson orbital variety

2003-11-26

arxiv.org/abs/math/0311474v1

Journal of Algebra 271, 2004, pp 698-724

Mathematics

Representation Theory

27 pages, to appear in Journal of Algebra

Scientific paper

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.

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