On the irreducibility of locally analytic principal series representations
Representation Theory
2011-01-19 v3
Abstract
Let G be a p-adic connected reductive group with Lie algebra g. For a parabolic subgroup P in G and a finite-dimensional locally analytic representation V of P, we study the induced locally analytic G-representation W = Ind^G_P(V). Our result is the following criterion concerning the topological irreducibility of W: if the Verma module U(g) \otimes_{U(p)} V' associated to the dual representation V' is irreducible then W is topologically irreducible as well.
Keywords
Cite
@article{arxiv.math/0612809,
title = {On the irreducibility of locally analytic principal series representations},
author = {S. Orlik and M. Strauch},
journal= {arXiv preprint arXiv:math/0612809},
year = {2011}
}
Comments
44 pages; final version. An appendix has been added in which it is shown that the canonical maps between certain completions of distribution algebras are injective. This fills a gap in a previous version; it was pointed out to us by a referee