Boundary unitary representations—right-angled hyperbolic buildings

Uri  Bader; Jan  Dymara

doi:10.3934/jmd.2016.10.413

Article Contents

2016, Volume 10: 413-437. Doi: 10.3934/jmd.2016.10.413

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Boundary unitary representations—right-angled hyperbolic buildings

Uri Bader^1, and
Jan Dymara^2,

1.
Department of Mathematics, The Weizmann Institute of Science, Rehovot, 7610001
2.
Instytut Matematyczny, Uniwersytet Wrocławski, pl. Grunwaldzki 2/4, 50-384 Wrocław

Received: May 31, 2015

Revised: June 30, 2016

Published: August 2016

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Abstract

We study the unitary boundary representation of a strongly transitive group acting on a right-angled hyperbolic building. We show its irreducibility. We do so by associating to such a representation a representation of a certain Hecke algebra, which is a deformation of the classical representation of a hyperbolic reflection group. We show that the associated Hecke algebra representation is irreducible.

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Mathematics Subject Classification: Primary: 22D10; Secondary: 20C08, 20E42.

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