Spectral analysis of the free orthogonal matrix

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

paper

Spectral analysis of the free orthogonal matrix

arXiv:0901.1918

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 $[- 2/ n + 2, 2/ n + 2]$ , 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 $S U_{2}^{q}$ due to Woronowicz, and several calculations with orthogonal polynomials.

22 pages, 4 figures