99 research outputs found
On orbital variety closures in sl(n). II. Descendants of a Richardson orbital variety
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.Comment: 27 pages, to appear in Journal of Algebr
B-orbits in abelian nilradicals of types B, C and D: towards a conjecture of Panyushev
Let be a Borel subgroup of a semisimple algebraic group and let
be an abelian nilradical in . Using
subsets of strongly orthogonal roots in the subset of positive roots
corresponding to , D. Panyushev \cite{Pan} gives in particular
classification of orbits in and and states
general conjectures on the closure and dimensions of the orbits in both
and in terms of involutions of the Weyl group.
Using Pyasetskii correspondence between orbits in and
he shows the equivalence of these two conjectures. In this
Note we prove his conjecture in types and for adjoint case.Comment: 12 page
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