What can one reconstruct from the representation ring of a compact group?

Details What can one reconstruct from the representation ring of a compact group? What can one reconstruct from the representation ring of a compact group?

2005-12-05

arxiv.org/abs/math/0512107v1

Proceedings of the 6th International Workshop on Lie Theory and Its Applications in Physics (15-21 August 2005, Varna, Bulgari

Mathematics

Group Theory

7 pages, to appear in the Proceedings of the 6th International Workshop on Lie Theory and Its Applications in Physics (15-21 A

Scientific paper

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.

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