On the irreducibility of locally analytic principal series representations

Details On the irreducibility of locally analytic principal series representations On the irreducibility of locally analytic principal series representations

2006-12-28

arxiv.org/abs/math/0612809v3

Representation Theory, Volume 14, pp. 713--746 (2010)

Mathematics

Representation Theory

44 pages; final version. An appendix has been added in which it is shown that the canonical maps between certain completions o

Scientific paper

10.1090/S1088-4165-2010-00387-8

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.

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