What can one reconstruct from the representation ring of a compact group?
Group Theory
2011-02-14 v1 Mathematical Physics
math.MP
Representation Theory
Abstract
It is well known that there exist non-isomorphic compact groups with isomorphic representation rings (fusion rules). Nevertheless, considerable structural information about the group can be reconstructed from its representation ring. We review these types of partial reconstruction theorems, including some recent results. In the Appendix a derivation of the Clebsch-Gordan series of SU(2) based only on information about the dimensions of the irreps is presented.
Cite
@article{arxiv.math/0512107,
title = {What can one reconstruct from the representation ring of a compact group?},
author = {Zoltan Zimboras},
journal= {arXiv preprint arXiv:math/0512107},
year = {2011}
}
Comments
7 pages, to appear in the Proceedings of the 6th International Workshop on Lie Theory and Its Applications in Physics (15-21 August 2005, Varna, Bulgaria)