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arXiv · 1607.05640

Box moves on Littlewood-Richardson tableaux and an application to invariant subspace varieties

Justyna Kosakowska·Markus Schmidmeier
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Abstract

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 first use partial maps on Littlewood-Richardson tableaux to generalize this result to finite direct sums of such embeddings. We then focus on an application to invariant subspaces of nilpotent linear operators. We develop a criterion to decide if two irreducible components in the representation space are in the boundary partial order.

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BibTeXRIS

Justyna Kosakowska, Markus Schmidmeier. 2016-07-19. Box moves on Littlewood-Richardson tableaux and an application to invariant subspace varieties. https://doi.org/10.1016/j.jalgebra.2017.07.025

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