Quivers, long exact sequences and Horn type inequalities II

TL;DR

This paper investigates the conditions under which a sequence of finite abelian p-groups can form a long exact sequence, extending results related to eigenvalues of Hermitian matrices to a broader algebraic context.

Contribution

It generalizes Horn type inequalities to classify possible types of finite abelian p-groups in long exact sequences, building on and extending Fulton's earlier work.

Findings

Characterization of all m-tuples forming long exact sequences of finite abelian p-groups

Extension of Horn inequalities to a new algebraic setting

Recovery of Fulton's results for the case m=3

Abstract

We study the set of all m-tuples $(\lambda(1),...,\lambda(m))$ of possible types of finite abelian p-groups $M_{\lambda(1)}, ..., M_{\lambda(m)}$ for which there exists a long exact sequence $M_{\lambda(1)} \to ... \to M_{\lambda(m)}$. When m=3, we recover Fulton's results on the possible eigenvalues of majorized Hermitian matrices.