A Characterization of the Irreducible Representations of the Group of Rotations
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Authors
Lipinski, Ronald L.
Issue Date
1973
Type
Thesis
Language
en_US
Keywords
Alternative Title
Abstract
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.
Description
iii, 28 p.
Citation
Publisher
Kalamazoo College
License
U.S. copyright laws protect this material. Commercial use or distribution of this material is not permitted without prior written permission of the copyright holder.