Components of the Springer Fiber and Domino Tableaux

Details Components of the Springer Fiber and Domino Tableaux Components of the Springer Fiber and Domino Tableaux

2002-10-27

arxiv.org/abs/math/0210416v1

Mathematics

Representation Theory

14 pages

Scientific paper

Consider a complex classical semi-simple Lie group along with the set of its nilpotent coadjoint orbits. When the group is of type A, the set of orbital varieties contained in a given nilpotent orbit is described a set of standard Young tableaux. We parameterize both, the orbital varieties and the irreducible components of unipotent varieties in the other classical groups by sets of standard domino tableaux. The main tools are Spaltenstein's results on signed domino tableaux together with Garfinkle's operations on standard domino tableaux.

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