Irreducible representations of the Cuntz algebra 𝒪_{𝒩}

Jeong, Eui-Chai

doi:10.1090/S0002-9939-99-05018-2

Irreducible representations of the Cuntz algebra $\mathcal {O}_N$
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by Eui-Chai Jeong

Proc. Amer. Math. Soc. 127 (1999), 3583-3590

DOI: https://doi.org/10.1090/S0002-9939-99-05018-2

Published electronically: May 17, 1999

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Abstract:

In this paper, we establish formulas for the configuration of a special class of irreducible representations of the Cuntz algebra $\mathcal {O}_{N}$, $N=2,3,\dots ,\infty$. These irreducible representations arise as subrepresentations of naturally occurring representations of $\mathcal {O}_{N}$ acting in $L^{2}\left ( \mathbb {T}\right )$ and arise from consideration of multiresolution wavelet filters.

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