Related papers: Distinguished Cuspidal Representations over p-adic…

We analyze reducibility points of representations of $p$-adic groups of classical type, induced from generic supercuspidal representations of maximal Levi subgroups, both on and off the unitary axis. We are able to give general, uniform…

Let $F$ be a non-archimedean local field. We show that any representation of a maximal compact subgroup of $\mathbf{SL}_N(F)$ which is typical for an essentially tame supercuspidal representation must be induced from a Bushnell--Kutzko…

We show that a compact representation of a semisimple Lie group has an orthogonal decomposition into finite length representations. This generalises and simplifies a number of more special spectral theorems in the literature. We apply it to…

This paper examines fields of rationality in families of cuspidal automorphic representations of unitary groups. Specifically, for a fixed $A$ and a sufficiently large family $\mathcal{F}$, a small proportion of representations $\pi\in…

We determine the decomposition of the restriction of a length-one toral supercuspidal representation of a connected reductive group to the algebraic derived subgroup, in terms of parametrizing data, and show this restriction has…

Let $D$ be the quatenion division algebra over a non-Archimedean local field $F$ of characteristic zero and odd residual characterisitc. We show that an irreducible discrete series representation of $\mathrm{GL}_n(D)$ is…

Quasirational presentations ($QR$-presentations) of (pro-$p$)groups are studied. Such presentations include, in particular, aspherical presentations of discrete groups and their subpresentations and pro-$p$-groups with a single defining…

Let G be the group of rational points of a connected reductive group over a finite field. Based on work of Lusztig and Yun, we make the Jordan decomposition for irreducible G-representations canonical. It comes in the form of an equivalence…

We show that subpresentations of aspherical prounipotent presentations over fields of zero characteristics and subpresentations of aspherical pro-$p$-presentations are aspherical, an application to subpresentations of aspherical discrete…

We give a criterion in terms of p-adic Asai L-functions for a cuspidal automorphic representation of GL(2) over a real quadratic field to be a distinguished representation, providing a p-adic counterpart of a well-known theorem of Flicker…

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…

In this paper we address the issue of existence of cusp forms for almost simple Lie groups using the approach of the second author combined with local information on supercuspidal representations for $p$-adic groups known by the first…

A method to construct irreducible unitary representations of a hyperspecial compact subgroup of a reductive group over p-adic field with odd p is presented. Our method is based upon Cliffods theory and Weil representations over finite…

Let $K$ be a local non-Archimedean field of positive characteristic and let $L$ be the degree-$n$ unramified extension of $K$. Via the local Langlands and Jacquet-Langlands correspondences, to each sufficiently generic multiplicative…

Representations of four-dimensional superconformal groups on harmonic superfields are discussed. It is argued that any representation can be given as a superfield on many superflag manifolds. Representations on analytic superspaces do not…

We discuss progress towards the classification of irreducible admissible representations of reductive groups over non-archimedean local fields and the local Langlands correspondence. We also state some (partly conjectural) compatibility…

In [HJLLZ24], we proposed a new conjecture on the structure of the unitary dual of connected reductive groups over non-Archimedean local fields of characteristic zero based on their Arthur representations and verified it for all the known…

We develop a theory of Anosov representation of geometrically finite Fuchsian groups in SL(d,R) and show that cusped Hitchin representations are Borel Anosov in this sense. We establish analogues of many properties of traditional Anosov…

We describe the supercuspidal representations of Sp(4,F), for F a non-archimedean local field of residual characteristic different from 2, and determine which are generic.

We present various results on disconnected reductive groups, in particular about the characteristic 0 representation theory of such groups over finite fields.