Abstract
In the article [Spa1], N. Spaltenstein has established a bijection between the irreducible components of F χ, the space of full flags fixed by a nilpotent element χ ϵ M( n, k), where k is an algebraically closed field, and the standard tableaux associated to the Young diagram of χ. In this present work we determine, when χ is of hook type, for each irreducible component X of F χ, the unique Schubert cell C X of the full flag manifold F = F ( V) (where V is vector space of dimension n over k), such that X ∩ C X is a dense subspace in X. This result will allow us to optimize the computation of F χ and when k = C is the complex field, to see that the graph resolution of the partition (2, 1, …, 1) of n is related to the Dynkin diagram of sl( n, C ).
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