We study components of the Bernstein decomposition of a p-adic classical group (with p odd) with inertial support a self-dual positive level supercuspidal representation of a Siegel Levi subgroup. More precisely, we use the method of covers to construct a Bushnell-Kutzko type for such a component. A detailed knowledge of the Hecke algebra of the type should have number-theoretic implications.

The aim of this paper is to prove two general results on parabolic induction of classical p-adic groups (actually, one of them holds also in the archimedean case), and to obtain from them some consequences about irreducible unitarizable representations. One of these consequences is a reduction of the unitarizability problem for these groups. This reduction is similar to the reduction of the uni...

This paper has two aims. The first is to give a description of irreducible tempered representations of classical p-adic groups which follows naturally the classification of irreducible square integrable representations modulo cuspidal data obtained in [15] and [19]. The second aim of the paper is to give description of an invariant (partially defined function) of irreducible square integrable r...

To an irreducible square integrable representation π of a classical p-adic group, C. Mœglin has attached invariants Jord(π), πcusp and ǫπ . These triples classify square integrable representations modulo cuspidal data (assuming a natural hypothesis). The definition of these invariants in [M] is rather simple in terms of induced representations, except at one case when a coherent normalization o...

Let Sn be either the group Sp(n) or SO(2n+1) over a p-adic field F . Then Levi factors of maximal parabolic subgroups are (isomorphic to) direct products of GL(k) and Sn−k , with 1 ≤ k ≤ n. The square integrable representations which we define and study in this paper (and prove their square integrability), are subquotients of reducible representations Indn P (δ⊗σ), where δ is an essentially squ...

We formulate a version of the o-minimal group conjectures from [11], which is appropriate for groups G definable in a (saturated) p-adically closed field K, We discuss the conjectures in two cases, when G is defined over Qp and when G is of the form E(K) for E an elliptic curve over K.

We construct an Euler system of p-adic zeta elements over the eigencurve which interpolates Kato’s zeta elements over all classical points. Applying a big regulator map gives rise to a purely algebraic construction of a two-variable p-adic L-function over the eigencurve. As a first application of these ideas, we prove the equality of the p-adic L-functions associated with a critical-slope refin...