## Abstract

Let n_{n}(ℂ) be the algebra of strictly upper-triangular n×n matrices and let X_{2} = {u ∈ n_{n}(ℂ) |u^{2} = 0} be the subset of matrices of nilpotent order 2. Let B _{n}(ℂ) be the group of invertible upper-triangular matrices acting on n_{n} by conjugation. Let B_{u} be the orbit of u ∈ X_{2} with respect to this action. Let S_{n}^{2} be the subset of involutions in the symmetric group S_{n} We define a new partial order on S_{n}^{2} which gives the combinatorial description of the closure of B_{u} We also construct an ideal I(B _{u})⊂ S(n^{*})whose variety V(I}(B_{u}) equals B_{u}. We apply these results to orbital varieties of nilpotent order 2 in sl_{n}(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