GIT-equivalence and semi-stable subcategories of quiver representations
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The main investigation in this thesis is to determine when two weights give rise to the same semi-stable subcategory in the case of representations of quivers. This question was answered via explicit construction by Ingalls, Paquette and Thomas in, for the case of tame quivers. It is answered here in greater generality using methods and ideas from invariant theory. Lastly, it is verified that the explicit construction given in agrees with the general result given here in the case that the quiver in question is tame.