Representations of The miraculous Klein group
Abstract
The Klein group contains only four elements. Nevertheless this little group contains a number of remarkable entry points to current highways of modern representation theory of groups. In this paper, we shall describe all possible ways in which the Klein group can act on vector spaces over a field of two elements. These are called representations of the Klein group. This description involves some powerful visual methods of representation theory which builds on the work of generations of mathematicians starting roughly with the work of K. Weiestrass. We also discuss some applications to properties of duality and Heller shifts of the representations of the Klein group.
 Publication:

arXiv eprints
 Pub Date:
 September 2012
 arXiv:
 arXiv:1209.4074
 Bibcode:
 2012arXiv1209.4074C
 Keywords:

 Mathematics  Representation Theory
 EPrint:
 Ramanujan Mathematics Society Newsletter 22 (2012), No. 1, 135145