Let Γ be a free nonabelian group and let Ω be its boundary. Let πh be one of the unitary representations of Γ introduced earlier by the authors in (1996, Duke Math. J.82, 381-436). By its definition πh acts on L2(Ω, dνh) for a certain measure νh. This gives a boundary realization of πh in a sense we make precise. We show that πh does not have any other boundary realizations and simultaneously provide a new proof that πh is irreducible. © 2000 Academic Press.
Kuhn, M., Steger, T. (2001). Monotony of certain free group representations. JOURNAL OF FUNCTIONAL ANALYSIS, 179(1), 1-17 [10.1006/jfan.2000.3663].
Monotony of certain free group representations
KUHN, MARIA GABRIELLA;
2001
Abstract
Let Γ be a free nonabelian group and let Ω be its boundary. Let πh be one of the unitary representations of Γ introduced earlier by the authors in (1996, Duke Math. J.82, 381-436). By its definition πh acts on L2(Ω, dνh) for a certain measure νh. This gives a boundary realization of πh in a sense we make precise. We show that πh does not have any other boundary realizations and simultaneously provide a new proof that πh is irreducible. © 2000 Academic Press.
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