Related papers: The endoscopic character identity for even special…

This article presents a 3-local characterisation of the sporadic simple group McL and its automorphism group. The theorem is underpinned by a further identification theorem the proof of which is character theoretic. The main theorem is…

We prove asymptotic upper bounds for the $L^2$ Betti numbers of the locally symmetric spaces associated to a quasi-split $U(4)$. These manifolds are 8-dimensional, and we prove bounds in degrees 2 and 3, with the behaviour in the other…

Since the study by Jacobi and Hecke, Hecke-type series have received a lot of attention. Unlike such series associated with indefinite quadratic forms, identities on Hecke-type series associated with definite quadratic forms are quite rare…

We begin this paper by reviewing the Langlands correspondence for unipotent representations of the exceptional group of type $G_2$ over a $p$-adic field $F$ and present it in an explicit form. Then we compute all ABV-packets, as defined in…

The goal of this paper is to prove how Arthur's results, in the case of split odd orthogonal p-adic groups, imply the Langlands' classification of discrete series. Of course this need the validity of ''fundamental'' lemmas which are not yet…

We prove that regular supercuspidal representations of $p$-adic groups are uniquely determined by their character values on very regular elements -- a special class of regular semisimple elements on which character formulae are very simple…

We generalize the work of M. Harris and R. Taylor on the local Langlands correspondence for the linear group over $\mathbb{Q}_p$. We prove some cases of the Kottwitz conjectures for the supercuspidal part of the compactly supported…

We show the existence of some non-classical cohomological p-adic automorphic eigenforms for SL(2) using endoscopy and the geometry of eigenvarieties. These forms seem to account for some non-automorphic members of classical global…

In this paper, we reformulate Moeglin's explicit construction of local A-packets of split odd special orthogonal groups and symplectic groups. By this reformulation together with results of the previous paper with Minguez, we can compute…

It has been shown by Nistor that given any extension of associative algebras over C, the connecting morphism in periodic cyclic homology is compatible, under the Chern-Connes character, with the index morphism in lower algebraic K-theory.…

We show that local-global compatibility (at split primes) away from $p$ holds at all points of the $p$-adic eigenvariety of a definite $n$-variable unitary group. The novelty is we allow non-classical points, possibly non-\'{e}tale over…

Let $X$ be a second countable locally compact Abelian group. We prove some group analogues of the Skitovich--Darmois, Heyde and Kac--Bernstein characterisation theorems for $Q$-independent random variables taking values in the group $X$.…

This (quasi-)survey addresses the quasi-isometry classification of locally compact groups, with an emphasis on amenable hyperbolic locally compact groups. This encompasses the problem of quasi-isometry classification of homogeneous…

We give a classification of the cuspidal automorphic representations attached to rational elliptic curves with a non-trivial torsion point of odd order. Such elliptic curves are parameterizable, and in this paper, we find the necessary and…

In arXiv:1208.1945, Shin and Templier proved certain equidistribution bounds on local components of certain families of automorphic representations. We extend their weight-aspect results to families of automorphic representations where the…

In this paper we use character variety methods to study homomorphisms between the fundamental groups of 3-manifolds, in particular those induced by non-zero degree maps. A {\it knot manifold} is a compact, connected, irreducible, orientable…

We elucidate the relationship between Schr\"odinger-cat-like macroscopicity and geometric entanglement, and argue that these quantities are not interchangeable. While both properties are lost due to decoherence, we show that macroscopicity…

We show that the identity component of the group of diffeomorphisms of a closed oriented surface of positive genus admits many unbounded quasi-morphisms. As a corollary, we also deduce that this group is not uniformly perfect and its…

We give a new Jacobi--Trudi-type formula for characters of finite-dimensional irreducible representations in type $C_n$ using characters of the fundamental representations and non-intersecting lattice paths. We give equivalent determinant…

Let $E$ be a non-Archimedian local field of characteristic zero and residue characteristic $p$. Let ${\bf G}$ be a connected reductive group defined over $E$ and $\pi$ an irreducible admissible representation of $G={\bf G}(E)$. A result of…