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Abstract
Let F be a p-adic field with uniformizer π. Given a smooth mod p-representation of G = GL2(F)/π, we consider its subspace of invariants under the action of the pro-p-Iwahori subgroup and get this way a functor taking values in the category of right modules over the pro-p-Hecke algebra with characteristic p. We show that if F = ℚp, this functor restricted to the representations generated by their pro-p-invariants is an equivalence of categories, and give examples of other p-adic fields for which it is not the case.
Received: 2006-04-03
Revised: 2008-05-01
Published Online: 2009-07-30
Published in Print: 2009-October
© Walter de Gruyter Berlin · New York 2009