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Special series of unitary representations of groups acting on homogeneous trees

Published online by Cambridge University Press:  09 April 2009

Anna Maria Mantero
Affiliation:
Istituto di Matematica, Via L. B. Alberti, 4 16132 Genova, Italy
Anna Zappa
Affiliation:
Istituto di Matematica, Via L. B. Alberti, 4 16132 Genova, Italy
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Abstract

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Let G be a group acting faithfully on a homogeneous tree of order p + 1, p > 1. Let be the space of functions on the Poission boundary ω, of zero mean on ω. When p is a prime. G is a discrete subgroup of PGL2(Qp) of finite covolume. The representations of the special series of PGL2(Qp), Which are irreducible and unitary in an appropriate completion of , are shown to be reducible when restricted to G. It is proved that these representations of G are algebraically reducible on and topologically irreducible on endowed with the week topology.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1986

References

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