# ERGODIC UNITARILY INVARIANT MEASURES ON THE SPACE OF INFINITE HERMITIAN MATRICES

@article{Olshanski1996ERGODICUI,
title={ERGODIC UNITARILY INVARIANT MEASURES ON THE SPACE OF INFINITE HERMITIAN MATRICES},
author={Grigori Olshanski and Anatolii Moiseevich Vershik},
journal={arXiv: Representation Theory},
year={1996}
}
• Published 7 January 1996
• Mathematics
• arXiv: Representation Theory
Let $H$ be the space of all Hermitian matrices of infinite order and $U(\infty)$ be the inductive limit of the chain $U(1)\subset U(2)\subset...$ of compact unitary groups. The group $U(\infty)$ operates on the space $H$ by conjugations, and our aim is to classify the ergodic $U(\infty)$-invariant probability measures on $H$ by making use of a general asymptotic approach proposed in Vershik's note \cite{V}. The problem is reduced to studying the limit behavior of orbital integrals of the form…
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