Spectral analysis of the free orthogonal matrix
Abstract
We compute the spectral measure of the standard generators uij of the Wang algebra Ao(n). We show in particular that this measure has support [-2/n+2,2/n+2], and that it has no atoms. The computation is done by using various techniques, involving the general Wang algebra Ao(F), a representation of SUq2 due to Woronowicz, and several calculations with orthogonal polynomials.
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