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Box moves on Littlewood-Richardson tableaux and an application to invariant subspace varieties
- Source :
- Journal of Algebra 491 (2017), 241-264
- Publication Year :
- 2016
-
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.
Details
- Database :
- arXiv
- Journal :
- Journal of Algebra 491 (2017), 241-264
- Publication Type :
- Report
- Accession number :
- edsarx.1607.05640
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2017.07.025