Related papers: The regular and profinite representations of resid…

Let $\mathfrak{o}$ be the ring of integers of a non-archimedean local field with the maximal ideal $\wp$ and the finite residue field of characteristic $p.$ Let $\mathbf{G}$ be the General Linear or Special Linear group with entries from…

We study parabolic G-Higgs bundles over a compact Riemann surface with fixed punctures, when G is a real reductive Lie group, and establish a correspondence between these objects and representations of the fundamental group of the punctured…

We introduce and develop a categorification of the theory of Real representations of finite groups. In particular, we generalize the categorical character theory of Ganter--Kapranov and Bartlett to the Real setting. Given a Real…

If G is a finite subgroup of the automorphism group of a projective curve X and D is a divisor on X stabilized by G, then under the assumption that D is nonspecial, we compute a simplified formula for the trace of the natural representation…

A universality of deformed Heisenberg algebra involving the reflection operator is revealed. It is shown that in addition to the well-known infinite-dimensional representations related to parabosons, the algebra has also finite-dimensional…

Let $n\le 5$ be an integer, and let $\Gamma$ be a finite group. We prove that if $\rho , \rho': \Gamma \to O(n)$ are two representations that are conjugate by an orientation-preserving diffeomorphism, then they are conjugate by an element…

A finite sampling theory associated with a unitary representation of a finite non Abelian group $\mathbf{G}$ on a Hilbert space is stablished. The non Abelian group $\mathbf{G}$ is a knit product $\mathbf{N}\bowtie \mathbf{H}$ of two finite…

By a "Boolean inverse semigroup" we mean an inverse semigroup whose semilattice of idempotents is a Boolean algebra. We study representations of a given inverse semigroup S in a Boolean inverse semigroup which are "tight" in a certain well…

The general linear group GL(n, K) over a field K contains a particularly prominent subgroup U(n, K), consisting of all the upper triangular unipotent elements. In this paper we are interested in the case when K is the finite field F_q, and…

Let $G$ be a real reductive Lie group and $H$ a reductive subgroup of $G$. Benoist-Kobayashi studied when $L^2(G/H)$ is a tempered representation of $G$ and in particular they gave a necessary and sufficient condition for the temperedness…

Let $\C$ be a variety of finite groups. We use profinite Bass--Serre theory to show that if $u:H\hookrightarrow G$ is a map of finitely generated residually $\C$ groups such that the induced map $\hat{u}:\hat{H}\rightarrow\hat{G}$ is a…

Given two Fuchsian representations $\rho_l$ and $\rho_r$ of the fundamental group of a closed oriented surface $S$ of genus $\geq 2$, we study the relation between Lagrangian submanifolds of $M_\rho=(\mathbb{H}^2/\rho_l(\pi_1(S)))\times…

Let G be a split connected reductive algebraic group over Q_p such that both G and its dual group G-hat have connected centres. Motivated by a hypothetical p-adic Langlands correspondence for G(Q_p) we associate to an n-dimensional ordinary…

We study basic properties of the category of smooth representations of a p-adic group G with coefficients in any commutative ring R in which p is invertible. Our main purpose is to prove that Hecke algebras are noetherian whenever R is ; a…

We study the subgroup structure, Hecke algebras, quasi-regular representations, and asymptotic properties of some fractal groups of branch type. We introduce parabolic subgroups, show that they are weakly maximal, and that the corresponding…

Let $G$ be a group that is relatively hyperbolic with respect to a collection of subgroups $\{H_{\lambda}\}_{\lambda\in \Lambda}$. Suppose that $G$ is given by a finite relative presentation $\mathcal{P}$ with respect to this collection. We…

Let $U$ be an algebraic subgroup of the group of $n\times n$ upper-triangular matrices with units on the diagonal over a finite field of large enough characteristic, and $\mathfrak{n}$ be the Lie algebra of $U$. The main tool in…

We establish new results on the weak containment of quasi-regular and Koopman representations of a second countable locally compact group $G$ associated with non-singular $G$-spaces. We deduce that any two boundary representations of a…

The problem of describing the group of units $\mathcal{U}(\mathbb{Z} G)$ of the integral group ring $\mathbb{Z} G$ of a finite group $G$ has attracted a lot of attention and providing presentations for such groups is a fundamental problem.…

For any homogeneous space of a noncompact semisimple Lie group $G$, we define an exponent with multiple interpretations from representation theory and group theory. As an application, we give a temperedness criterion for $L^2 (G/H)$ for any…