Dimension vectors in regular components over wild Kronecker quivers

2012/09/04 by Chen, Bo
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1209.0612

Abstract

Let K_n be the so-called wild Kronecker quiver, i.e., a quiver with one source and one sink and n≥ 3 arrows from the source to the sink. The following problems will be studied for an arbitrary regular component C of the Auslander-Reiten quiver: (1) What is the relationship between dimension vectors and quasi-lengths of the indecomposable regular representations in C? (2) For a given natural number d, is there an upper bound of the number of indecomposable representations in C with the same length d? (3) When do the sets of the dimension vectors of indecomposable representations in different regular components coincide?

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