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• W2951874411 abstract "We study a class of representations of the Cuntz algebras O_N, N=2,3,..., acting on L^2(T) where T=R/2pi 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_Nsubset 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." @default.
• W2951874411 created "2019-06-27" @default.
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• W2951874411 date "1996-12-17" @default.
• W2951874411 modified "2023-09-27" @default.
• W2951874411 title "Iterated function systems and permutation representations of the Cuntz algebra" @default.
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