On orbital variety closures in sln III. Geometric properties

摘要: Abstract This is the third paper in series. Here we define a few combinatorial orders on Young tableaux. The first order obtained from induced Duflo by extension with help of Vogan T α , β procedure. We call it Duflo–Vogan order. second generalization Spaltenstein's construction consideration an orbital variety as double chain nilpotent orbits. Again, use Vogan's procedure, however, this time to restrict Vogan-chain tableaux defined inclusion closures called geometric and inverse primitive ideals algebraic get following relations between orders: order; and, finally, computations show that coincide sl n for ⩽ 9 = 10 there one case (up procedure transposition) where chain-Vogan proper In only coincides These permit us conjecture As well combinatorics both inclusions