Description of B−orbit Closures of Order 2 in Upper-triangular Matrices

@inproceedings{Melnikov2008DescriptionOB,
  title={Description of B−orbit Closures of Order 2 in Upper-triangular Matrices},
  author={Anna Melnikov},
  year={2008}
}
Abstract. Let nn(C) be an algebra of strictly upper-triangular n × n matrices and X2 = {u ∈ nn(C) : u2 = 0} be the subset of matrices of nilpotent order 2. Let Bn(C) be the group of invertible upper-triangular matrices acting on nn by conjugation. For Bu an orbit of u ∈ X2 with respect to this action we give the combinatorial description of the closure of Bu and construct an ideal IBu ⊂ S(n ) such that its variety V(IBu) = Bu. We apply these results to orbital varieties of nilpotent order 2 in… CONTINUE READING

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