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Bulgarian Journal of Physics
Print: 1310-0157 Online: 1314-2666
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RECOGNIZED BY THE EUROPEAN PHYSICAL SOCIETY 
Bulg. J. Phys. vol.33 no.s2 (2006), pp. 76-82
What Can One Reconstruct from the Representation Ring of a Compact Group?
Z. Zimborás
Research Institute for Particle and Nuclear Physics, P.O. Box 49, H-1525 Budapest, Hungary
go backResearch Institute for Particle and Nuclear Physics, P.O. Box 49, H-1525 Budapest, Hungary
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 irreducible representations is presented.