On orbital variety closures in sl(n). I. Induced Duflo order

Details On orbital variety closures in sl(n). I. Induced Duflo order On orbital variety closures in sl(n). I. Induced Duflo order

2003-11-26

arxiv.org/abs/math/0311472v1

Journal of Algebra, 271, 2004, pp. 179-233

Mathematics

Representation Theory

55 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. Inclusion relation on orbital variety closures defines a partial order on Young tableaux. Our aim is to describe this order. The paper is devoted to the combinatorial description of induced Duflo order on Young tableaux (the order generated by inclusion of generating subspaces of orbital varieties). This is a very interesting and complex combinatorial question. This is the first paper in the series. In Part II and Part III we use repeatedly the results of the paper as a basis for further study of orbital variety closures.

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