In this paper the authors generalize a result of Vogan on irreducibility of standard modules for generic representations from real groups to p-adic ones whenever the inducing data is supercuspidal. They also prove injectivity for standard modules in this case. As applications, the authors prove a number of results relating the poles of intertwining operators and points of reducibility of induce...

We examine the theory of induced representations for non-connected reductive p-adic groups for which G/G is abelian. We first examine the structure of those representations of the form IndGP 0(σ), where P 0 is a parabolic subgroup of G and σ is a discrete series representation of the Levi component of P . Here we develop a theory of R–groups, extending the theory in the connected case. We then ...

This paper is concerned with representations of split orthogonal and quasi-split unitary groups over a nonarchimedean local field which are not generic, but which support a unique model of a different kind, the generalized Bessel model. The properties of the Bessel models under induction are studied, and an analogue of Rodier’s theorem concerning the induction of Whittaker models is proved for ...

We analyze the geometry of the tower of LubinTate deformation spaces, which parametrize deformations of a onedimensional formal module of height h together with level structure. According to the conjecture of Deligne-Carayol, these spaces realize the local Langlands correspondence in their l-adic cohomology. This conjecture is now a theorem, but currently there is no purely local proof. Working...

Let $F$ be a non-archimedean local field of odd characteristic $p > 0$. In this paper, we consider exterior square $L$-functions $L(s,\pi,\wedge^2)$, Bump-Friedberg $L(s,\pi,BF)$, and Asai $L(s,\pi,As)$ an irreducible admissible representation $\pi$ $GL_m(F)$. particular, establish that those $L$-functions, via the theory integral representations, are equal to their corresponding Artin $L(s,\we...

In this paper we provide a geometric framework for the study of characters of depth-zero representations of unramified groups over local fields with finite residue fields which is built directly on Lusztig's theory of character sheaves for groups over finite fields. We introduce depth-zero character sheaves, which are coefficient systems of ℓ-adic sheaves on Bruhat-Tits buildings for p-adic gro...

Abstract For a connected reductive group G defined over non-archimedean local field F , we consider the Bernstein blocks in category of smooth representations G ⁢ ( F stretchy="false">) {G(F)} . whose cuspidal support involves regular sup...

Let G be a simple algebraic group defined over the global field k. In this paper, we use the simple trace formula to determine the sum of the multiplicities of the irreducible representations in the cuspidal spectrum of G, with specified local behavior at a finite set of places of k and unramified elsewhere. This sum is expressed as the product of the values of modified Artin L-functions at neg...

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.