A Characterization of the Irreducible Representations of the Group of Rotations
Lipinski, Ronald L.
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The theory of group representation is a powerful synthesis of the properties of matrices and groups. It was developed at the turn of the century by the German mathematician F.G. Frobenius. Several contributions were also made by I. Schur. Representation theory is perhaps the most important application of group theory. It reduces the abstract properties of groups to numbers. It accomplishes this through the use of a homomorphism between the elements of a group and linear transformations in some linear space. Thus since every linear transformation in a finite space has a matrix corresponding to it, we see the importance of matrix theory to representation theory. In the following discussion, we will be concerned with the group of rotations. My main research source was an article by I.M. Gel'Fand and Z.Ya. Sapio entitled Representations of the Group of Rotations of 3-dimensional Space and Their Application. This article details a method of describing all of the representations of the rotation group of 3-dimensional space.