On the restriction of representations of GL2(F) to a Borel subgroup

Vytautas Paskunas

doi:10.1112/S0010437X07002862

On the restriction of representations of GL2(F) to a Borel subgroup

Part of: Lie groups

Published online by Cambridge University Press: 01 November 2007

Vytautas Paskunas

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Vytautas Paskunas*: Affiliation:
Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany (email: [email protected])

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Abstract

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Abstract

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Let F be a non-Archimedean local field and let p be the residual characteristic of F. Let G=GL2(F) and let P be a Borel subgroup of G. In this paper we study the restriction of irreducible smooth representations of G on -vector spaces to P. We show that in a certain sense P controls the representation theory of G. We then extend our results to smooth -modules of finite length and unitary K-Banach space representations of G, where is the ring of integers of a complete discretely valued field K with residue field .