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arXiv · 1601.01931

Radial parts of Haar measures and probability distributions on the space of rational matrix-valued functions

Yury A. Neretin
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Abstract

Consider the space $C$ of conjugacy classes of a unitary group $U(n+m)$ with respect to a smaller unitary group $U(m)$. It is known that for any element of the space $C$ we can assign canonically a matrix-valued rational function on the Riemann sphere (a Livshits characteristic function). In the paper we write an explicit expression for the natural measure on $C$ obtained as the pushforward of the Haar measure of the group $U(n+m)$ in the terms of characteristic functions.

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Yury A. Neretin. 2016-01-08. Radial parts of Haar measures and probability distributions on the space of rational matrix-valued functions. https://doi.org/10.4213/im8467%2C%2010.1070%2Fim8467

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