Strongly nilpotent matrices and Gelfand–Zetlin modules Original Research Article

Let image be the variety of n×n matrices, which k×k submatrices, formed by the first k rows and columns, are nilpotent for any k=1,…,n. We show, that Xn is a complete intersection of dimension (n−1)n/2 and deduce from it, that every character of the Gelfand–Zetlin subalgebra in U(gln) extends to an irreducible representation of U(gln).