Related papers: A local Langlands correspondence for unipotent rep…

We characterize the Local Langlands Correspondence (LLC) for inner forms of $GL_n$ via the Jacquet-Langlands Correspondence (JLC) and compatibility with the Langlands Classification. We show that LLC satisfies a natural compatibility with…

Let G be a split connected reductive group over a local non-archimedean field. We classify all irreducible complex G-representations in the principal series, irrespective of the (dis)connectedness of the centre of G. This leads to a local…

We construct the Lafforgue variety, an affine scheme equipped with an open dense subscheme parametrizing the simple modules of a non-commutative unital algebra $R$ over any field $k$, provided that the center $Z(R)$ is finitely generated…

We describe the image, under the local Langlands correspondence for tori, of the characters of a torus which are trivial on its Iwahori subgroup. Let $k$ be a non-archimedian local field. Let $\boldsymbol{G}$ be a connected reductive group…

The formal degree of a unipotent discrete series character of a simple linear algebraic group over a non-archimedean local field (in the sense of Lusztig), is a rational function of the cardinality q of the residue field. The irreducible…

In all forms of the local Langlands program the abelian category of smooth representations of p-adic groups G in vector spaces over a field k plays a central role. Of particular interest are its finiteness properties. If the field k has…

In this paper we show a local Jacquet-Langlands correspondence for all unitary irreducible representations. We prove the global Jacquet-Langlands correspondence in characteristic zero. As consequences we obtain the multiplicity one and…

We review the construction of generalized affine Hecke algebras attached to Bernstein series of both smooth irreducible and enhanced $L$-parameters of $p$-adic reductive groups and apply it to the study of the Howe correspondence.

The first part of this article is a review of the properties expected of any local Langlands correspondence that aims to be considered "canonical," and of known results that establish some or all of these properties for specific groups. In…

Let $F$ be a non-Archimedean local field and $G$ be the general linear group $\mathrm{GL}_n$ over $F$. Based on the previous results of the author, we can describe the Langlands parameter of an essentially tame supercuspidal representation…

We propose a geometric strategy of giving explicit description of the Langlands parameter of an irreducible supercuspidal representation of GL(n) over a non-archimedean local field. The key is to compare the cohomology of an affinoid in the…

In the present article we define coverings of affine Deligne-Lusztig varieties attached to a connected reductive group over a local field of characteristic $p > 0$. In the case of $\GL_2$, the unramified part of the local Langlands…

The Bruhat-Tits theory is a key ingredient in the construction of irreducible smooth representations of $p$-adic reductive groups. We describe generalizations to arbitrary such representations of several results recently obtained in the…

Let F be a non-Archimedean local field and let G be a connected reductive affine algebraic F-group. Let I be an Iwahori subgroup of G(F) and denote by H(G; I) the Iwahori-Hecke algebra, i.e. the convolution algebra of complex-valued…

We prove that the reduction mod \ell of the local Langlands correspondence between supercuspidal representations of GL_n(F), where F is a finite extension of Q_p, and representations of the Galois group of F is well-defined. The results and…

We prove a number of unconditional statistical results of the Hecke coefficients for unitary cuspidal representations of $\operatorname{GL}(2)$ over number fields. Using partial bounds on the size of the Hecke coefficients, instances of…

Let G be a reductive algebraic group over the algebraic closure of a finite field F_q of good characteristic. In this paper, we demonstrate a remarkable compatibility between the Springer correspondence for G and the parametrization of…

Let $F$ be a non-Archimedean locally compact field, let $G$ be a split connected reductive group over $F$. For a parabolic subgroup $Q\subset G$ and a ring $L$ we consider the $G$-representation on the $L$-module$$(*)\quad\quad\quad\quad…

Let F be a non-archimedean local field with residue characteristic p. Let l be a prime number different from p. Let G be a connected reductive group which is split, semi-simple, and simply connected. On the one hand, we describe the…

Selfdual representations of any group fall into two classes when they are irreducible: those which carry a symmetric bilinear form, and the others which carry an alternating bilinear form. The Langlands correspondence, which matches the…