- 00-438 Palle E. T. Jorgensen
- Representations of Cuntz algebras, loop groups and wavelets
(21K, LaTeX2e amsproc class, 6 pages)
Nov 8, 00
(auto. generated ps),
of related papers
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.