B-orbits of nilpotency order 2 and link patterns

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Let Bn be the group of upper-triangular invertible n×n matrices and Xn be the set of strictly upper triangular n×n matrices of square zero seen as an algebraic variety. Bn acts on Xn by conjugation. In this paper we give first results on the geometry of orbits Xn/Bn in terms of link patterns.Further we apply this description to the computations of the closures of orbital varieties of nilpotency order 2 and their pairwise intersections. In particular, we connect our results on intersections to the combinatorics of meanders in Temperley-Lieb algebras and pairwise intersections of the components of a Springer fiber over a nilpotent element with two Jordan blocks.

Original languageEnglish
Pages (from-to)443-473
Number of pages31
JournalIndagationes Mathematicae
Issue number2
StatePublished - Mar 2013


  • Borel adjoint orbits
  • Involutions and link patterns
  • Orbital varieties
  • Young tableaux

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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