 00438 Palle E. T. Jorgensen
 Representations of Cuntz algebras, loop groups and wavelets
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Nov 8, 00

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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 infinitedimensional loop group.
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