Journal of Modern Dynamics (JMD)

Boundary unitary representations—right-angled hyperbolic buildings

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

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Uri Bader - Department of Mathematics, The Weizmann Institute of Science, Rehovot, 7610001, Israel (email)
Jan Dymara - Instytut Matematyczny, Uniwersytet Wrocławski, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland (email)

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.

Keywords:  Unitary representation, hyperbolic building, Hecke algebra.
Mathematics Subject Classification:  Primary: 22D10; Secondary: 20C08, 20E42.

Received: June 2015;      Revised: July 2016;      Available Online: September 2016.