Related papers: Ordinary $GL_2(F)$-representations in characterist…

Let F be a local field of characteristic 0. The Breuil-Schneider conjecture for GL_2(F) predicts which locally algebraic representations of this group admit an integral structure. We extend the methods of [K-dS12], which treated smooth…

The restriction of a supercuspidal representation of SL_2(k), for k a local nonarchimedean field, to a maximal compact subgroup decomposes as a multiplicity-free direct sum of irreducible representations. We explicitly describe this…

The character formulas of Sally and Shalika are an early triumph in $p$-adic harmonic analysis, but, to date, the calculations underlying the formulas have not been available. In this paper, which should be viewed as a precursor of the…

Let $F/F_0$ be a quadratic extension of non-Archimedean locally compact fields of residual characteristic $p\neq2$ with Galois automorphism $\sigma$, and let $R$ be an algebraically closed field of characteristic $\ell\notin\{0,p\}$. We…

We present some unpublished results of Kutzko together with results of Hill, giving a classification of the smooth (complex) representations of $\mathrm{GL}_{2}(\mathcal{O})$, where $\mathcal{O}$ is the ring of integers in a local field…

Representations of the non-semisimple superalgebra $gl(2|2)$ in the standard basis are investigated by means of the vector coherent state method and boson-fermion realization. All finite-dimensional irreducible typical and atypical…

We study components of the Bernstein category for 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…

Let $F$ be a non-archimedean local field. The classification of the irreducible representations of $GL_n(F)$, $n\ge0$ in terms of supercuspidal representations is one of the highlights of the Bernstein--Zelevinsky theory. We give an…

We investigate the mod-$p$ supersingular representations of $GL_2(D)$, where $D$ is a division algebra over a $p$-adic field with characteristic 0, by computing a basis for the vector space of the pro-$p$ Iwahori subgroup invariants of a…

We prove various results about the Local Converse Problem for split reductive groups $G$ over a non-archimedean local field~$F$ of characteristic $0$ and residual characteristic $p$. In particular, we prove that when $G$ is a symplectic or…

Let $F/F_0$ be a quadratic extension of non-Archimedean locally compact fields with residual characteristic $p\neq2$, and $\ell$ be a prime number different from $p$. We classify those $\ell$-modular cuspidal irreducible representations of…

The local Langlands correspondence for GL(n) of a non-Archimedean local field $F$ parametrizes irreducible admissible representations of $GL(n,F)$ in terms of representations of the Weil-Deligne group $WD_F$ of $F$. The correspondence,…

Following what Barthel-Livn\'e and Breuil made for GL(2,F), we study mod $p$ representations of SL(2,F) for F a complete non-archimedean local field of residual characteristic p and with finite residue field. In particular, we link these…

Let G be a reductive group over the field F=k((t)), where k is an algebraic closure of a finite field, and let W be the (extended) affine Weyl group of G. The associated affine Deligne-Lusztig varieties $X_x(b)$, which are indexed by…

For a classical group over a non-archimedean local field of odd residual characteristic p, we construct all cuspidal representations over an arbitrary algebraically closed field of characteristic different from p, as representations induced…

In a previous article, a universal linear algebraic model was proposed for describing homogeneous conformal geometries, such as the spherical, Euclidean, hyperbolic, Minkowski, anti-de Sitter and Galilei planes. This formalism was…

Let G be a connected reductive group over a non-archimedean local field K, and assume that G splits over an unramified extension of K. We establish a local Langlands correspondence for irreducible unipotent representations of G. It comes as…

Building on prior work, we analyze the decomposition of the restriction of an irreducible representation of SL_2(k), for k a p-adic field of odd residual characteristic, to a maximal compact subgroup K. The pattern of the decomposition…

The main question we are going to address in this paper is: How much does the representation theory of the $p$-adic group $\mathrm{GL}_n(\mathcal{D})$ depend on the $p$-adic division algebra $\mathcal{D}$? Let $\mathcal{D}$ be a central…

We show that $L$-packets of toral supercuspidal representations arising from unramified maximal tori of $p$-adic groups are realized by Deligne--Lusztig varieties for parahoric subgroups. We prove this by exhibiting a direct comparison…