Palle E. T. Jorgensen
Representations of Cuntz algebras, loop groups and wavelets
(21K, LaTeX2e amsproc class, 6 pages)

ABSTRACT.  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.