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Abstract: We show that the category of representations of the Euclidean group oforientation-preserving isometries of two-dimensional Euclidean space isequivalent to the category of representations of the preprojective algebra ofinfinite type A. We also consider the moduli space of representations of theEuclidean group along with a set of generators. We show that these modulispaces are quiver varieties of the type considered by Nakajima. Using theseidentifications, we prove various results about the representation theory ofthe Euclidean group. In particular, we prove it is of wild representation typebut that if we impose certain restrictions on weight decompositions, we obtainonly a finite number of indecomposable representations.



Author: Alistair Savage

Source: https://arxiv.org/







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