Applications of Littlewood-Richardson tableaux to computing generic extension of semisimple invariant subspaces of nilpotent linear operators

Abstract

The main aim of the paper is to present a combinatorial algorithm that, applying Littlewood-Richardson tableaux with entries equal to 1, computes generic extensions of semisimple invariant subspaces of nilpotent linear operators. Moreover, we discuss geometric properties of generic extensions and their connections with combinatorics.