The entries in the LR-tableau

Details The entries in the LR-tableau The entries in the LR-tableau

2009-03-23

arxiv.org/abs/0903.3790v2

Mathematics

Representation Theory

14 pages, the proof of Theorem 1 is simplified

Scientific paper

Let $\Gamma$ be the Littlewood-Richardson tableau corresponding to an embedding $M$ of a subgroup in a finite abelian $p$-group. Each individual entry in $\Gamma$ yields information about the homomorphisms from $M$ into a particular subgroup embedding, and hence determines the position of $M$ within the category of subgroup embeddings. Conversely, this category provides a categorification for LR-tableaux in the sense that all subgroup embeddings corresponding to a given LR-tableau share certain homological properties.

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