Quivers, long exact sequences and Horn type inequalities

Details Quivers, long exact sequences and Horn type inequalities Quivers, long exact sequences and Horn type inequalities

2004-10-19

arxiv.org/abs/math/0410423v3

Mathematics

Representation Theory

29 pages

Scientific paper

We give necessary and sufficient inequalities for the existence of long exact sequences of m finite abelian p-groups with fixed isomorphy types. This problem is related to some generalized Littlewood-Richardson coefficients that we define in this paper. We also show how this problem is related to eigenvalues of Hermitian matrices satisfying certain (in)equalities. When m=3, we recover the Horn type inequalities that solve the saturation conjecture for Littlewood-Richardson coefficients and Horn's conjecture.

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