Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Iterated function systems and permutation representations of the Cuntz
  algebra   We study a class of representations of the Cuntz algebras O_N, N=2,3,...,
acting on L^2(T) where T=R/2\pi Z. The representations arise in wavelet theory,
but are of independent interest. We find and describe the decomposition into
irreducibles, and show how the O_N-irreducibles decompose when restricted to
the subalgebra UHF_N\subset O_N of gauge-invariant elements; and we show that
the whole structure is accounted for by arithmetic and combinatorial properties
of the integers Z. We have general results on a class of representations of O_N
on Hilbert space H such that the generators S_i as operators permute the
elements in some orthonormal basis for H. We then use this to extend our
results from L^2(T) to L^2(T^d), d>1 ; even to L^2(\mathbf{T}) where \mathbf{T}
is some fractal version of the torus which carries more of the algebraic
information encoded in our representations.

16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th