The entries in the LR-tableau

Abstract

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.

14 pages, the proof of Theorem 1 is simplified

References in corpus (2)

• Invariant Subspaces of Nilpotent Linear Operators. I
• The Auslander-Reiten Translation in Submodule Categories

Cited by in corpus (4)

• The boundary of the irreducible components for invariant subspace varieties
• Hall polynomials via automorphisms of short exact sequences
• The socle tableau as a dual version of the Littlewood-Richardson tableau
• Two Partial Orders for Standard Young Tableaux