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arXiv · 0901.1918

Spectral analysis of the free orthogonal matrix

T. Banica·B. Collins·P. Zinn-Justin
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Abstract

We compute the spectral measure of the standard generators $u_{ij}$ of the Wang algebra $A_o(n)$. We show in particular that this measure has support $[-2/\sqrt{n+2},2/\sqrt{n+2}]$, and that it has no atoms. The computation is done by using various techniques, involving the general Wang algebra $A_o(F)$, a representation of $SU^q_2$ due to Woronowicz, and several calculations with orthogonal polynomials.

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T. Banica, B. Collins, P. Zinn-Justin. 2009-03-30. Spectral analysis of the free orthogonal matrix. https://arxiv.org/abs/0901.1918

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