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Boundary unitary representations—right-angled hyperbolic buildings

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


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