We discuss some application of Jacquet modules in the study of parabolically induced representations of classical p-adic groups. The main problem that we consider is the construction of non-cuspidal square integrable representations. Since the problem is related to understanding of the reducibilityof the parabolically induced representations, we discuss also the reducibility questions.

Introduction. The problem of classifying the tempered spectrum of a connected reductive quasi-split group, defined over a local field, F, of characteristic zero, consists of three parts. The first is to classify the discrete series representations of any Levi subgroup. The second step is to understand the rank one Plancherel measures, which is equivalent to understanding the reducibility of tho...

In this paper, we give an explicit computable algorithm for the Zelevinsky–Aubert duals of irreducible representations $p$ -adic symplectic and odd special orthogonal groups. To do this, establish formulas certain derivatives socles. We also a combinatorial criterion irreducibility parabolically induced representations.

In this paper, we consider representations of p p -adic classical groups parabolically induced from the products shifted Speh and unitary Arth...

In this paper we study reducibility of those representations of quasi-split unitary p-adic groups which are parabolically induced from supercuspidal representations of general linear groups. For a supercuspidal representation associated via Howe’s construction to an admissible character, we show that in many cases a criterion of Goldberg for reducibility of the induced representation reduces to...

Preface 1 1. Classical groups 4 2. Parabolic induction 10 3. Admissible representations 16 4. Jacquet modules and cuspidal representations 24 5. Composition series of induced representations of SL(2, F ) and GL(2, F ) 34 6. Some examples 39 7. Parabolically induced representations of SL(2, F ) and GL(2, F ) 45 8. Some general consequences 52 9. GL(n, F ) 55 10. GSp(n, F ) 62 11. On the reducibi...

Cuspidal representations of a reductive p-adic group G over a field of characteristic different from p are relatively injective and projective with respect to extensions that split by a U-equivariant linear map for any subgroup U that is compact modulo the centre. The category of smooth representations over a field whose characteristic does not divide the pro-order of G is the product of the su...

Let K/F be a quadratic extension of p-adic fields. The Bernstein-Zelevinsky’s classification asserts that generic representations are parabolically induced from quasi-squareintegrable representations. We show, following a method developed by Cogdell and PiatetskiShapiro, that expected equality of the Rankin-Selberg type Asai L-function of a generic representation of GL(n, K), and the Asai L-fun...