Abstract
Let nn(ℂ) be the algebra of strictly upper-triangular n×n matrices and let X2 = {u ∈ nn(ℂ) |u2 = 0} be the subset of matrices of nilpotent order 2. Let B n(ℂ) be the group of invertible upper-triangular matrices acting on nn by conjugation. Let Bu be the orbit of u ∈ X2 with respect to this action. Let Sn2 be the subset of involutions in the symmetric group Sn We define a new partial order on Sn2 which gives the combinatorial description of the closure of Bu We also construct an ideal I(B u)⊂ S(n*)whose variety V(I}(Bu) equals Bu. We apply these results to orbital varieties of nilpotent order 2 in sln(ℂ)in order to give a complete combinatorial description of the closure of such an orbital variety in terms of Young tableaux. We also construct the ideal of definition of such an orbital variety up to taking the radical.
Original language | English |
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Pages (from-to) | 217-247 |
Number of pages | 31 |
Journal | Transformation Groups |
Volume | 11 |
Issue number | 2 |
DOIs | |
State | Published - Jun 2006 |
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology