Related papers: A Product Theorem in simple Lie groups

A random Lie group action on a compact manifold generates a discrete time Markov process. The main object of this paper is the evaluation of associated Birkhoff sums in a regime of weak, but sufficiently effective coupling of the…

We prove a generalization of a conjecture of C. Marion on generation properties of finite groups of Lie type, by considering geometric properties of an appropriate representation variety and associated tangent spaces.

The Liebeck-Nikolov-Shalev conjecture [LNS12] asserts that, for any finite simple non-abelian group $G$ and any set $A\subseteq G$ with $|A|\geq 2$, $G$ is the product of at most $N\frac{\log|G|}{\log|A|}$ conjugates of $A$, for some…

We prove an extension of Bourgain's theorem on pinned distances in measurable subset of $\mathbb{R}^2$ of positive upper density, namely Theorem $1^\prime$ in [Bourgain, 1986], to pinned non-degenerate $k$-dimensional simplices in…

In this paper we continue the study of groups of trace class and consider in particular the case of semi-direct products. One of the highlights is the theorem saying that the semi-direct product of a semisimple Lie group G and its Lie…

We show that every admissible irreducible representation of a product of two locally compact groups is a tensor product of admissible irreducible representations of the factors.

We prove a generalized Fej\'er's theorem for locally compact groups.

In this article we define the twisted product of groups as the generalization of the semidirect product of groups. We will find the necessary and sufficient condition in order that the twisted product of groups to be a group. In particular,…

We generalize Mertens' product theorem to Chebotarev sets of prime ideals in Galois extensions of number fields. Using work of Rosen, we extend an argument of Williams from cyclotomic extensions to this more general case. Additionally, we…

The main aim of this paper is to determine the multiplicative lie algebra structures on the semi-direct product of an abelian group with a group under certain conditions.

A form of Williamson's product theorem which applies to Williamson matrices of even order is presented.

We give a new proof of the discretized ring theorem for sets of real numbers. As a special case, we show that if $A\subset\mathbb{R}$ is a $(\delta,1/2)_1$-set in the sense of Katz and Tao, then either $A+A$ or $A.A$ must have measure at…

In this paper, we strengthen the splitting theorem proved in [14, 15] and provide a different approach using ideas from the weak KAM theory.

We formulate and prove a twofold generalisation of Lie's second theorem that integrates homomorphisms between formal group laws to homomorphisms between Lie groups. Firstly we generalise classical Lie theory by replacing groups with…

In this paper, we give the central limit theorem and almost sure central limit theorem for products of some partial sums of independent identically distributed random variables.

Let $\mathfrak{g}$ be an algebra over $K$ with a bilinear operation $[\cdot,\cdot]:\mathfrak{g}\times\mathfrak{g}\rightarrow\mathfrak{g}$ not necessarily associative. For $A\subseteq\mathfrak{g}$, let $A^{k}$ be the set of elements of…

The Morimoto theorem states that each connected abelian complex Lie group $A$ can be decomposed into the direct product of a group on which all holomorphic functions are constant, finitely many copies of $\mathbb{C}^\times$ and a vector…

We prove an analogue of the fixed-point theorem for the case of definably amenable groups.

We introduce a special class of multiple Dirichlet series whose terms are supported on a variety and which admit an Euler product structure. We proposed several conjectures on the analytic properties of these series.

We show that Hardy's uncertainty principle can be reformulated in such a way that it has an analogue even for compact Lie groups and symmetric spaces of compact type.