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On the restriction of representations of GL2(F) to a Borel subgroup
- Part of
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- Journal:
- Compositio Mathematica / Volume 143 / Issue 6 / November 2007
- Published online by Cambridge University Press:
- 01 November 2007, pp. 1533-1544
- Print publication:
- November 2007
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- Article
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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 .
-vector spaces to 
-modules of finite length and unitary 
is the ring of integers of a complete discretely valued field 