Spectral analysis of the free orthogonal matrix

Details Spectral analysis of the free orthogonal matrix Spectral analysis of the free orthogonal matrix

2009-01-14

arxiv.org/abs/0901.1918v2

Int. Math. Res. Not. 17 (2009), 3286-3309

Mathematics

Operator Algebras

22 pages, 4 figures

Scientific paper

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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