Related papers: Estimates of automorphic forms on $\mathrm{SU}(n,1…

Although the hyperbolic metric possesses many remarkable properties, it is not defined on arbitrary subdomains of $\mathbb{R}^n$ with $n \geq 2$. This article introduces a new hyperbolic-type metric that provides an alternative approach to…

We consider the hypercube in $\mathbb R^n$, and show that its quantum symmetry group is a $q$-deformation of $O_n$ at $q=-1$. Then we consider the graph formed by $n$ segments, and show that its quantum symmetry group is free in some…

We propose a practical recipe to compute the ${s}$-parametrized maps for systems with $SU(1,1)$ symmetry using a connection between the ${Q}$ and ${P} $ symbols through the action of an operator invariant under the group. The particular…

Let $\Gamma$ be a hyperbolic group and G be the isometry group of a Gromov-hyperbolic, properand geodesic metric space. We study the action of the outer automorphism group Out($\Gamma$) onthe set X($\Gamma$,G) of conjugacy classes of…

We define a set of holomorphic functions in terms of the Hauptmodul of a quotient Riemann surface and prove that these functions are holomorphic on the upper half-plane. It is also shown that these functions are automorphic forms of weight…

A gauge invariant mathematical formalism based on deformation quantization is outlined to model an $\mathcal{N}=2$ supersymmetric system of a spin $1/2$ charged particle placed in a nocommutative plane under the influence of a vertical…

In this paper, we study the relationship between the type problem and the asymptotic behavior of the first eigenvalues $\lambda_1(B_r)$ of ``balls'' $B_r:=\{\rho<r\}$ on a complete Riemannian manfold $M$ as $r\rightarrow +\infty$, where…

On a family of arithmetic hyperbolic 3-manifolds of squarefree level, we prove an upper bound for the sup-norm of Hecke-Maass cusp forms, with a power saving over the local geometric bound simultaneously in the Laplacian eigenvalue and the…

We study superpaticle models with fermionic gauge symmetry on the coset spaces of the $SU(1,1|N)$ supergroup. We first construct $SU(1,1|N)$ supersymmetric extension of a particle on $AdS_2$ possessing the $\kappa$-symmetry. Including…

Suppose that $\Gamma=(V,E)$ is a graph with vertices $V$, edges $E$, a free group action on the vertices $\mathbb{Z}^d \curvearrowright V$ with finitely many orbits, and a linear operator $D$ on the Hilbert space $l^2(V)$ such that $D$…

Let M be a compact 3-manifold whose interior admits a complete hyperbolic structure. We let Lambda(M) be the supremum of the bottom eigenvalue of the Laplacian of N, where N varies over all hyperbolic 3-manifolds homeomorphic to the…

Given a non-trivial complete valued field $K$ with value group $\Lambda$, we construct a $\Lambda$-tree space associated to $K$ analog of the Bruhat-Tits tree, and locally finite trees associated to compact subsets of the projective line.…

A group $H \cong {\mathbb Z}_{k}^{2g}$, where $g,k \geq 2$ are integers, of conformal automorphisms of a closed Riemann surface $S$ is called a $(g,k)$-Fermat group if it acts freely with quotient $S/H$ of genus $g$. We study some…

In this paper we consider the integral orthogonal group with respect to the quadratic form of signature $(2,3)$ given by $\left(\begin{smallmatrix} 0 & 1 \\ 1 & 0 \end{smallmatrix}\right) \perp \left(\begin{smallmatrix} 0 & 1 \\ 1 & 0…

We study the analytic torsion of odd-dimensional hyperbolic orbifolds $\Gamma \backslash \mathbb{H}^{2n+1}$, depending on a representation of $\Gamma$. Our main goal is to understand the asymptotic behavior of the analytic torsion with…

Let $G=PSL(2,\mathbb{R})$, let $\Gamma$ be a lattice in $G$, and let $\mathcal{H}$ be an irreducible unitary representation of $G$ with square-integrable matrix coefficients. A theorem in [Goodman, de la Harpe, Jones 1989] states that the…

Let $M$ be a complex manifold and $L$ be a line bundle over $M$ with a Hermitian metric $h$ whose Chern form is a K\"ahler form $\omega$. Let $X \subset M$ be a Lagrangian submanifold of $(M, \omega)$. When $X$ satisfies the Bohr-Sommerfeld…

In this paper we study the integrability of a family of models with U(1)xSU(N) symmetry. They admit fermionic and bosonic formulations related through bosonization and subsequent T-duality. The fermionic theory is just the CP^(N-1) sigma…

The Cl(3,0) Clifford algebra is represented with the commutative ring of hyperbolic numbers H. The canonical form of the Poincare mass operator defined in this vector space corresponds to a sixteen-dimensional structure. This conflicts with…

We begin the investigation of Gamma-limit groups, where Gamma is a torsion-free group which is hyperbolic relative to a collection of free abelian subgroups. Using the results of Drutu and Sapir, we adapt the results from math.GR/0404440 to…