A class of nonunitary, finite dimensional representations of the euclidean algebra e(2)

In this article, we examine the. nite dimensional representations of the Euclidean algebra e (2) that are obtained by embedding e(2) into sl(3), the Lie algebra of traceless 3 x 3 matrices. We show that the. nite dimensional, irreducible representations of sl(3) restricted to e(2) are indecomposable and, when possible, we give graphical descriptions of these e (2) representations.