[Persistent Müllerian ducts syndrome].
Persistent Müllerian ducts syndrome is a rare form of internal male pseudohermaphroditism, characterized by the presence of the uterus, fallopian tubes and upper vagina in an otherwise normally virilised male with a 46 XY karyotype. It is the result of a deficiency in anti-Müllerian hormone or abnormality of this hormone receptor. Often, the diagnosis is made incidentally during surgical exploration for cryptorchidism or herniorrhaphy, and exceptionally during cancer of ectopic testis. We discuss a rare case of this syndrome revealed by a bilateral intra-abdominal gonadal tumor.
We study multiple orthogonal polynomials of Meixner-Pollaczek type with respect to a symmetric system of two orthogonality measures. Our main result is that the limiting distribution of the zeros of these polynomials is one component of the solution to a constrained vector equilibrium problem. We also provide a Rodrigues formula and closed expressions for the recurrence coefficients. The proof of the main result follows from a connection with the eigenvalues of block Toeplitz matrices, for which we provide some general results of independent interest. ::: The motivation for this paper is the study of a model in statistical mechanics, the so-called six-vertex model with domain wall boundary conditions, in a particular regime known as the free fermion line. We show how the multiple Meixner-Pollaczek polynomials arise in an inhomogeneous version of this model.