Radial parts of Haar measures and probability distributions on the space of rational matrix-valued functionsстатья
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Аннотация:We consider the space C of conjugacy classes of the unitary group U(n+m) with respect to a smaller unitary group U(m). It is known that to every element of C we can canonically assign a rational matrix-valued function (the Livshits characteristic function) on the Riemann sphere. We find an explicit expression for the natural measure on C obtained as the push-forward of the Haar measure of U(n+m) in terms of characteristic functions