Mathematics – Functional Analysis
Scientific paper
2000-08-15
XIIIth International Congress on Mathematical Physics (London, 2000) (A. Fokas, A. Grigoryan, T. Kibble, and B. Zegarlinski, e
Mathematics
Functional Analysis
6 pages, LaTeX2e "amsproc" class; expanded version of an invited lecture given by the author at the International Congress on
Scientific paper
A theorem of Glimm states that representation theory of an NGCR C*-algebra is always intractable, and the Cuntz algebra O_N is a case in point. The equivalence classes of irreducible representations under unitary equivalence cannot be captured with a Borel cross section. Nonetheless, we prove here that wavelet representations correspond to equivalence classes of irreducible representations of O_N, and they are effectively labeled by elements of the loop group, i.e., the group of measurable functions A:T-->U_N(C). These representations of O_N are constructed here from an orbit picture analysis of the infinite-dimensional loop group.
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