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Irreducibility of the analytic continuation of the principal series of a free group

Part of: Abstract harmonic analysis Lie groups

Published online by Cambridge University Press:  09 April 2009

Anna Maria Mantero  and
Anna Zappa
Anna Maria Mantero
Affiliation:
Istituto di Matematica Universita di GenovaVia L. B. Alberti 16132 Genova, Italy
Anna Zappa
Affiliation:
Istituto di Matematica Universita di GenovaVia L. B. Alberti 16132 Genova, Italy
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Abstract

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In this paper it is proved that the principal series of representations of Γ = Z2*…*Z2 may be analytically continued to give uniformly bounded representations on the same Hilbert space, and that these representations are irreducible. Further, the reducibility of the restrictions to Γ ⊂ SL(2, Qp) of the irreducible unitary representations of SL(2, Qp) is examined.

MSC classification

Secondary: 43A65: Representations of groups, semigroups, etc. 22E35: Analysis on $p$-adic Lie groups 22E40: Discrete subgroups of Lie groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 43 , Issue 2 , October 1987 , pp. 199 - 210
Copyright
Copyright © Australian Mathematical Society 1987

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