Emerton's Jacquet functors for non-Borel parabolic subgroups

Abstract

This paper studies Emerton's Jacquet module functor for locally analytic representations of p-adic reductive groups. When P is a parabolic subgroup whose Levi factor M is not commutative, we show that passing to an isotypical subspace for the derived subgroup of M gives rise to essentially admissible locally analytic representations of the torus Z(M), which have a natural interpretation in terms of rigid geometry. We use this to extend Emerton's representation-theoretic construction of eigenvarieties by constructing eigenvarieties interpolating automorphic representations whose local components at p are not necessarily principal series.

25 pages

References in corpus (1)

• Construction of eigenvarieties in small cohomological dimensions for semi-simple, simply connected groups

Cited by in corpus (3)

• Sur un problème de compatibilité local-global localement analytique
• Some results on locally analytic socle for ${\mathrm{GL}}_n({\mathbb{Q}}_p)$
• P-adic interpolation of metaplectic forms of cohomological type