Related papers: Reflection groups of Lorentzian lattices
This is the second in a series of papers that develops the theory of reflection monoids, motivated by the theory of reflection groups. Reflection monoids were first introduced in arXiv:0812.2789. In this paper we study their presentations…
We show that there are infinitely many commensurability classes of pseudomodular groups, thus answering a question raised by Long and Reid. These are Fuchsian groups whose cusp set is all of the rationals but which are not commensurable to…
We describe a general procedure to produce fundamental domains for complex hyperbolic triangle groups, a class of groups that contains a representative of the commensurability class of every known non-arithmetic lattice in ${\rm PU}(2,1)$.…
We present a new notion of non-positively curved groups: the collection of discrete countable groups acting (AU-)acylindrically on finite products of $\delta$-hyperbolic spaces with general type factors and associated subdirect products.…
Given an irreducible well-generated complex reflection group, we construct an explicit basis for the module of vector fields with logarithmic poles along its reflection arrangement. This construction yields in particular a Hodge filtration…
In this paper we classify reflection subgroups of Euclidean Coxeter groups.
Cais and Liu extended the theory of Kisin modules and crystalline representations to allow more general coefficient fields and lifts of Frobenius. Based on their theory, we classify lattices in crystalline representations by Kisin modules…
I briefly review early and recent progress concerning the dynamical properties of bulges. I also show results from a study on the kinematics of bulges and disks in edge-on galaxies, where the bulge rotation curve is obtained with little…
We introduce a new class of algebras called Poisson orders. This class includes the symplectic reflection algebras of Etingof and Ginzburg, many quantum groups at roots of unity, and enveloping algebras of restricted Lie algebras in…
A modular form on an even lattice $M$ of signature $(l,2)$ is called reflective if it vanishes only on quadratic divisors orthogonal to roots of $M$. In this paper we show that every reflective modular form on a lattice of type $2U\oplus L$…
We predict new phenomena, such as soliton steering and soliton fission, in optical lattices that fade away exponentially along the propagation direction. Such lattices, featuring tunable decay rates, arise in photorefractive crystals in the…
The goal of this paper is to show that many key results found in the study of Einstein Lorentzian nilpotent Lie algebras can still hold in the more general settings of unimodular Lie algebras and (completely) solvable Lie algebras.
We survey the existing parts of a classification of finite groups generated by orthogonal transformations in a finite-dimensional Euclidean space whose fixed point subspace has codimension one or two and extend it to a complete…
Algebraic lattices are those obtained from modules in the ring of integers of algebraic number fields through the canonical or twisted embeddings. In turn, well-rounded lattices are those with maximal cardinality of linearly independent…
The aim of this note is to give a geometric proof for classical local rigidity of lattices in semisimple Lie groups. We are reproving well known results in a more geometric (and hopefully clearer) way.
The concept of reflection positivity has its origins in the work of Osterwalder--Schrader on constructive quantum field theory. It is a fundamental tool to construct a relativistic quantum field theory as a unitary representation of the…
Clusters of galaxies have a huge mass which can act as gravitational lenses. Galaxies behind clusters can be distorted to form arcs in images by the lenses. Herein a search was done for giant lensed arcs by galaxy clusters using the SDSS…
The concepts of symmetry and symmetry groups are at the heart of several developments in modern theoretical and mathematical physics. The present paper is devoted to a number of selected topics within this framework: Euclidean and rotation…
Topological defects such as quantized vortices are one of the most striking manifestations of the superfluid nature of Bose-Einstein condensates and typical examples of quantum mechanical phenomena on a macroscopic scale. Here we…
We make various short points on the phenomenon of centre dominance in SU(2). The Z(2) dominance seen in Wilson loops is related to the loop distribution and to half-odd-integer representations of the group. The distributions also make it…