Spectral analysis of the free orthogonal matrix

T. Banica; B. Collins; P. Zinn-Justin

Spectral analysis of the free orthogonal matrix

Operator Algebras 2009-08-17 v2 Mathematical Physics math.MP

Authors: T. Banica , B. Collins , P. Zinn-Justin

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.

Keywords

spectral measure free orthogonal matrix Wang algebra orthogonal polynomials quantum group

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@article{arxiv.0901.1918,
  title  = {Spectral analysis of the free orthogonal matrix},
  author = {T. Banica and B. Collins and P. Zinn-Justin},
  journal= {arXiv preprint arXiv:0901.1918},
  year   = {2009}
}

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22 pages, 4 figures

Spectral analysis of the free orthogonal matrix

Abstract

Keywords

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