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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Restriction of spherical representations of $ {\rm PGL}\sb{2}({\bf Q}\sb{p})$ to a discrete subgroup


Authors: Alessandro Figà-Talamanca and Massimo A. Picardello
Journal: Proc. Amer. Math. Soc. 91 (1984), 405-408
MSC: Primary 22E50; Secondary 22E35, 43A65, 43A90
MathSciNet review: 744639
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Abstract: We study the action on the homogeneous tree associated with $ {\text{PG}}{{\text{L}}_2}({{\mathbf{Q}}_p})$, of a suitably chosen discrete subgroup which is isomorphic to $ {{\mathbf{Z}}_2} * \cdots * {{\mathbf{Z}}_2}$ and is cocompact. We prove that the spherical representations of $ {\text{PG}}{{\text{L}}_2}({{\mathbf{Q}}_p})$ remain irreducible when restricted to this subgroup.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0744639-3
PII: S 0002-9939(1984)0744639-3
Article copyright: © Copyright 1984 American Mathematical Society