Related papers: Criteria for the Existence of Cuspidal Theta Repre…

Let $G$ be a reductive $p$-adic group. We prove that all supercuspidal representations of $G$ arise through Yu's construction subject to certain hypotheses on $k$ (depending on $G$). As a corollary, under the same hypotheses, we see that…

This paper studies the behavior of Jiu-Kang Yu's tame supercuspidal representations relative to involutions of reductive p-adic groups. Symmetric space methods are used to illuminate various aspects of Yu's construction. Necessary…

Let G be a unitary, symplectic or special orthogonal group over a locally compact non-archimedean local field of odd residual characteristic. We construct many new supercuspidal representations of G, and Bushnell-Kutzko types for these…

We study the theta lifting for real unitary groups and completely determine the theta lifts of discrete series representations. In particular, we show that these theta lifts can be expressed as cohomologically induced representations in the…

Let F be a totally real number field, n a prime integer, and G a unitary group of rank n defined over F that is compact at every infinite place. We prove an asymptotic formula for the number of cuspidal automorphic representations of G…

Howe and Tan (1993) investigated a degenerate principal series representation of indefinite orthogonal groups $\mathrm{O}(V)$ and explicitly described its composition series. They showed that there exists a unique unitarizable irreducible…

We construct local and global metaplectic double covers of odd general spin groups, using the cover of Matsumoto of spin groups. Following Kazhdan and Patterson, a local exceptional representation is the unique irreducible quotient of a…

We show that, in good residual characteristic, most supercuspidal representations of a tamely ramified reductive p-adic group G arise from pairs (S,\theta), where S is a tame elliptic maximal torus of G, and \theta is a character of S…

This manuscript has two goals: 1. To write an explicit description of the degenerate residual spectrum of the split, simple, simply-connected, exceptional groups of type $E_n$ (for $n=6,7,8$). 2. To set a practical guide for similar…

Let $G$ be a reductive group over a nonarchimedean local field $F$. In the quest for a classification of irreducible smooth representations of $G$, it is critical to understand the case of supercuspidal representations -- those whose matrix…

We classify globally irreducible representations of alternating groups and double covers of symmetric and alternating groups. In order to achieve this classification we also completely characterise irreducible representations of such groups…

In this paper, we prove that theta correspondence preserves unitarity under certain restrictions.

Let $G$ be a split reductive $p$-adic Lie group. This paper is the first in a series on the construction of locally analytic $G$-representations which do not lie in the principal series. Here we consider the case of the general linear group…

This paper presents a natural generalisation of Saxl conjecture from a Lie-theoretical perspective, which is verified for the exceptional types. For classical types, progress is made using spin representations, revealing connections to…

We investigate the irreducible cuspidal $C$-representations of a reductive $p$-adic group $G$ over a field $C$ of characteristic different from $p$. When $C$ is algebraically closed, for many groups $G$, a list of cuspidal $C$-types…

This text is a response to the following question: What are the methods to build supercuspidal complex representations of p-adic reductive groups and are there ties between them ? We will give an overview of the Bushnell-Kutzko and Yu…

We study the theta lifting for real unitary groups and completely determine the theta lifts of tempered representations. In particular, we show that the theta lifts of (limits of) discrete series representations can be expressed as…

Let $\mathbf{F}_{4}$ be the unique (up to isomorphism) connected semisimple algebraic group over $\mathbb{Q}$ of type $\mathrm{F}_{4}$, with compact real points and split over $\mathbb{Q}_{p}$ for all primes $p$. A conjectural computation…

Theta series for exceptional groups have been suggested as a possible description of the eleven-dimensional quantum supermembrane. We present explicit formulae for these automorphic forms whenever the underlying Lie group $G$ is split (or…

We develop the theory of maximal representations of the fundamental group of a compact connected oriented surface with boundary, into a group of Hermitian type. For any such representation we define the Toledo invariant, for which we…