Related papers: Property RD and hypercontractivity for orthogonal …

This work concerns a generalization of property (RD) from discrete groups to twisted \'etale groupoids equipped with a length function. We show that, under the assumption that the \'etale groupoid is principal, twisted property (RD) is…

We discuss recent results on fluctuations of conserved charges, and their approach to the hadron resonance gas at temperatures below the chiral crossover (Tc) as well as to a gas of free quarks at very high temperatures. We will focus on…

This is the second in a series of papers about torsion-free groups which act properly and cocompactly on a CAT(0) metric space with isolated flats and relatively thin triangles. Our approach is to adapt the methods of Sela and others for…

The purpose of this paper is to study property (RD) for locally compact Hecke pairs. We discuss length functions on Hecke pairs and the growth of Hecke pairs. We establish an equivalence between property (RD) of locally compact groups and…

Every discrete group with Kazhdan's Property (T) is a quotient of a torsion-free, word hyperbolic group with Property (T).

We consider two random group models: the hexagonal model and the square model, defined as the quotient of a free group by a random set of reduced words of length four and six respectively. Our first main result is that in this model there…

We show that the the shift on the reduced C*--algebras of RD--groups, including the free group on infinitely many generators, and the amalgamated free product C*--algebras, enjoys the very strong ergodic property of the convergence to the…

In this article, we consider tensor products of unitary representations by irreducible non-unitary finite dimensional representations of topological groups to define a property that is a twisting of Kazhdan's Property (T). We use the…

Let $A$ be a finite dimensional $Q-$algebra and $\Gamma subset A$ a $Z-$order. We classify those $A$ with the property that $Z^2$ does not embed in $\mathcal{U}(\Gamma)$. We call this last property the hyperbolic property. We apply this in…

Let $X$ be an abstract orientable not necessarily compact CR manifold of dimension $2n+1$, $n\geq1$, and let $L^k$ be the $k$-th tensor power of a CR complex line bundle $L$ over $X$. Suppose that condition $Y(q)$ holds at each point of…

We show that the orthogonal free quantum groups are not inner amenable and we construct an explicit proper cocycle weakly contained in the regular representation. This strengthens the result of Vaes and the second author, showing that the…

A countable discrete group $\Gamma$ is said to have the relative ISR-property if for every non-trivial normal subgroup $N\trianglelefteq\Gamma$ and every von Neumann subalgebra $\mathcal{M}\subseteq L(\Gamma)$ invariant under conjugation by…

The Hardy-Littlewood inequality on $\mathbb{T}$ compares the $L^p$-norm of a function with a weighted $\ell^p$-norm of its Fourier coefficients. The approach has recently been studied for compact homogeneous spaces and we study a natural…

In this paper, we study the geometric property (T) for discretized warped cones of an action on a compact Lie group $M$ by its finitely generated subgroup. We show that if a subgroup $G$ is dense in $M$, then the associated discretized…

We describe the application of renormalization group improved perturbative QCD to inelastic lepton-hadron scattering at high center-of-mass energy but comparatively low photon virtuality. We construct a high energy factorization theorem…

We investigate the rigidity and asymptotic properties of quantum SU(2) representations of mapping class groups. In the spherical braid group case the trivial representation is not isolated in the family of quantum SU(2) representations. In…

Let $M$ be a complete non-compact manifold satisfying the volume doubling condition, with doubling index $N$ and reverse doubling index $n$, $n\le N$, both for large balls. Assume a Gaussian upper bound for the heat kernel, and an…

A two-leg quenched random bond disordered antiferromagnetic spin$-1/2$ Heisenberg ladder system is investigated by means of stochastic series expansion (SSE) quantum Monte Carlo (QMC) method. Thermal properties of the uniform and staggered…

In this paper we study twisted conjugacy classes and the $R_{\infty}$-property for classical linear groups. In particular, we prove that the general linear group ${\rm GL}_n(K)$ and the special linear group ${\rm SL}_n(K)$ possess…

The hypercontractive inequality is a fundamental result in analysis, with many applications throughout discrete mathematics, theoretical computer science, combinatorics and more. So far, variants of this inequality have been proved mainly…