2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59727A 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.6 pages, LaTeX2e "amsproc" class; expanded version of an invited lecture given by the author at the International Congress on Mathematical Physics, July 2000 in LondonFunctional AnalysisMathematical Physics46L60, 47D25, 42A16, 43A65 (Primary); 46L45, 42A65, 41A15 (Secondary)text