Restriction of spherical representations of 𝑃𝐺𝐿₂(𝑄_{𝑝}) to a discrete subgroup

Figà-Talamanca, Alessandro; Picardello, Massimo A.

doi:10.1090/S0002-9939-1984-0744639-3

Restriction of spherical representations of $\textrm {PGL}_{2}(\textbf {Q}_{p})$ to a discrete subgroup
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by Alessandro Figà-Talamanca and Massimo A. Picardello

Proc. Amer. Math. Soc. 91 (1984), 405-408

DOI: https://doi.org/10.1090/S0002-9939-1984-0744639-3

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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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