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We first review a constructive proof of Gabriel's theorem on the representation finiteness of Dynkin quivers for the case of an equioriented quiver of type  D . Then, we proceed to the analysis of polystable representations of such a quiver, give a direct proof of the characterisation of its semistable representations, and explain how we may recover a theorem of Abeasis and Koike from this characterisation . Finally, we illustrate how these results may be applied to the study of moduli spaces of quiver bundles.

linear and multilinear algebra

An elementary discussion of the representation and geometric invariant theory of equioriented quivers of type  D  with an application to quiver bundles