This paper gives a p-adic analogue of the Mackey theory, which relates representations of a group of type G = H×tA to systems of imprimitivity.

Let L 6= Qp be a proper finite field extension of Qp and o ⊂ L its ring of integers viewed as an abelian locally L-analytic group. Let ô be the rigid L-analytic group parametrizing the locally analytic characters of o constructed by Schneider-Teitelbaum. Let K/L be a finite extension field. We show that the base change ôK has a Picard group Pic(ôK) which is profinite and that the unit section i...

Let G be a unitary, symplectic or orthogonal group over a non-archimedean local field of residual characteristic different from 2, considered as the fixed point subgroup in a general linear group G̃ of an involution. Following [7] and [13], we generalize the notion of a semisimple character for G̃ and for G. In particular, following the formalism of [4], we show that these semisimple characters h...

Let π1,…,πk be smooth irreducible representations of p-adic general linear groups. We prove that the parabolic induction product π1×⋯×πk has a unique quotient whose Langlands parameter is sum parameters all factors (cyclicity property), assuming same property holds for each products πi×πj (i<j), and but at most two πi×πi remains (square-irreducibility property). Our technique applies recently d...