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Representations of Cuntz algebras, loop groups and wavelets

Palle E. T. Jorgensen
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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 infinite-dimensional loop group.

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Palle E. T. Jorgensen. 2000-08-15. Representations of Cuntz algebras, loop groups and wavelets. https://arxiv.org/abs/math/0008102

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