Finite direct sums of cyclic embeddings and an application to invariant subspace varieties

Justyna Kosakowska, Markus Schmidmeier

Published 2016-07-19Version 1

In his 1951 book "Infinite Abelian Groups", Kaplansky gives a combinatorial characterization of the isomorphism types of embeddings of a cyclic subgroup in a finite abelian group. In this paper we use partial maps on Littlewood-Richardson tableaux to generalize this result to finite direct sums of such embeddings. As an application to invariant subspaces of nilpotent linear operators, we develop a critereon to decide if two irreducible components in the representation space are in the boundary partial order.