Related papers: Micro-packets containing generic representations

Let $\overrightarrow{G}$ be a directed graph with no component of orderless than~$3$, and let $\Gamma$ be a finite Abelian group such that $|\Gamma|\geq 4|V(\overrightarrow{G})|$ or if $|V(\overrightarrow{G})|$ is large enough with respect…

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…

The global Langlands conjecture for $\text{GL}_n$ over a number field $F$ predicts a correspondence between certain algebraic automorphic representations $\pi$ of $\text{GL}_n(\mathbb{A}_F)$ and certain families $\{ \rho_{\pi,\ell} \}_\ell$…

A system of interacting atoms is represented as an union of two subsystems, one of which is the system of atoms, and the other is an auxiliary scalar covariant field, which is equivalent to a given static interatomic potential of general…

Let $\mathbf{G}$ be a connected reductive algebraic group over an algebraic closure $\overline{\mathbb{F}_p}$ of the finite field of prime order $p$ and let $F : \mathbf{G} \to \mathbf{G}$ be a Frobenius endomorphism with $G = \mathbf{G}^F$…

In a recent paper, Gross and Reeder study arithmetic properties of discrete Langlands parameters for semi-simple p-adic groups and conjecture that a special class of these -- the simple wild parameters -- should correspond to L-packets…

An \emph{$H$-packing} in a graph $G$ is a collection of pairwise vertex-disjoint copies of $H$ in $G$. We prove that for every $c > 0$ and every bipartite graph $H$, any $\lfloor cn \rfloor$-regular graph $G$ admits an $H$-packing that…

We explicitly compute the adjoint L-function of those L-packets of representations of the group GSp(4) over a p-adic field of characteristic zero that contain non-supercuspidal representations. As an application we verify a conjecture of…

Motivated by the study of the interrelation between functorial and algebraic quantum field theory, we point out that on any locally trivial bundle of compact groups, representations up to homotopy are enough to separate points by means of…

The Green-Griffiths-Lang conjecture says that for every complex projective algebraic variety $X$ of general type there exists a proper algebraic subvariety of $X$ containing all nonconstant entire holomorphic curves $f:\mathbb{C} \to X$.…

We classify what we call ``typically almost symmetric'' depth zero supercuspidal representations of classical groups into L-packets. Our main results resolve an ambiguity in the paper of Lust-Stevens \cite{Lust-Stevens} in this case, where…

It is proved that an endomorphism $\varphi$ of a hyperbolic group $G$ satisfies a H\"older condition with respect to a visual metric if and only if $\varphi$ is virtually injective and $G\varphi$ is a quasiconvex subgroup of $G$. If $G$ is…

We give a partial solution to a long-standing open problem in the theory of quantum groups, namely we prove that all finite-dimensional representations of a wide class of locally compact quantum groups factor through matrix quantum groups…

Let $\mathfrak{R}$ and $\mathfrak{R}'$ be two associative rings (not necessarily with the identity elements). A bijective map $\varphi$ of $\mathfrak{R}$ onto $\mathfrak{R}'$ is called a \textit{$m$-multiplicative isomorphism} if {$\varphi…

In 2006, Boyarchenko and Drinfeld conjectured that for a unipotent algebraic group over a field of positive characteristic, every geometric point is contained in the neutral connected component of its centralizer if and only if its…

The general form of the operators commuting with the ground representation (appearing in many physical problems within single particle approximation) of the group is found. With help of the modified group projector technique, this result is…

By virtue of the well-known theorem, a structure Lie group K of a principal bundle $P$ is reducible to its closed subgroup H iff there exists a global section of the quotient bundle P/K. In gauge theory, such sections are treated as Higgs…

Let K $\subset$ G be compact connected Lie groups with common maximal torus T. Let (M, $\omega$) be a prequantisable compact connected symplectic manifold with a Hamiltonian G-action. Geometric quantisation gives a virtual representation of…

Let $G$ be a $p$-divisible group over a complete discrete valuation ring $R$ of characteristic $p$. The generic fiber of $G$ determines a Galois representation $\rho$. The image of $\rho$ admits a ramification filtration and a Lie…

Unitary representations of the fundamental group of a Kahler manifold correspond to polystable vector bundles (with vanishing Chern classes). Semisimple linear representations correspond to polystable Higgs bundles. In this paper we find…