Boundary unitary representations - right-angled hyperbolic buildings

2015/06/20 by Uri Bader, Bader, Uri, Jan Dymara +1
Mathematics · #Advanced Algebra and Geometry #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.DS #math.GR #math.RT #msc:20 #msc:37

paper · pdf · doi:10.48550/arxiv.1506.06290

18 pages

arxiv created 2015/06/20 · arxiv updated 2015/06/23

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.

Related

• Boundaries of right-angled hyperbolic buildings
• Factorial multiparameter Hecke von Neumann algebras and representations of groups acting on right-angled buildings
• Boundary representations of hyperbolic groups
• Strongly convergent unitary representations of right-angled Artin groups
• Strongly transitive actions on Euclidean buildings