%0 Journal Article
%T Orthogonal polynomials on the unit circle, $q$-Gamma weights, and discrete Painlev¨¦ equations
%A Philippe Biane
%J Mathematics
%D 2009
%I arXiv
%X We consider orthogonal polynomials on the unit circle with respect to a weight which is a quotient of $q$-gamma functions. We show that the Verblunsky coefficients of these polynomials satisfy discrete Painlev\'e equations, in a Lax form, which correspond to an $A_3^{(1)}$ surface in Sakai's classification.
%U http://arxiv.org/abs/0901.0947v2