Related papers: Virtually special non-finitely presented groups vi…

We determine precisely the number of irreducible summands of an irreducible cross characteristic representation of $GL_{n}(q)$ on restriction to $SL_{n}(q)$. Combined with a recent result of C. Bonnafe, this yields a canonical labeling for…

We give an algorithm that decides whether a single equation in a group that is virtually a class $2$ nilpotent group with a virtually cyclic commutator subgroup, such as the Heisenberg group, admits a solution. This generalises the work of…

In this paper we use techniques from convex projective geometry to produce many new examples of thin subgroups of lattices in special linear groups that are isomorphic to the fundamental groups of finite volume hyperbolic manifolds. More…

Let $V$ be a finite abelian group of odd order, equipped with a non-degenerate, alternating form $\omega\colon V\times V \to \mathbb{Z}/m\mathbb{Z}$. We give closed formulas for the character values of the Weil representation associated…

We prove the existence of a limit shape and give its explicit description for certain probability distribution on signatures (or highest weights for unitary groups). The distributions have representation theoretic origin-they encode…

In this note, we show that the satisfiability of equations and inequations with recognisable constraints is decidable in groups that are virtually direct products of finitely many hyperbolic groups.

We show (using results of Wise and of Woodhouse) that a tubular group is always virtually special (meaning that it has a finite index subgroup embedding in a RAAG) if the underlying graph is a tree. We also adapt Gardam and Woodhouse's…

This thesis addresses questions in representation and invariant theory of finite groups. The first concerns singularities of quotient spaces under actions of finite groups. We introduce a class of finite groups such that the quotients have…

We exhibit a family of metrizable manifolds such that any finite group appears as the fundamental group of one of them. These spaces are especially interesting as they can be easily visualized, as opposed to classical examples of spaces…

Virtual singular braids are generalizations of singular braids and virtual braids. We define the virtual singular braid monoid via generators and relations, and prove Alexander- and Markov-type theorems for virtual singular links. We also…

We study the problem of deciding whether or not the image of an irreducible representation of the braid group $\B_3$ of degree $\leq 5$ has finite image if we are only given the eigenvalues of a generator. We provide a partial algorithm…

A recurring theme in finite group theory is understanding how the structure of a finite group is determined by the arithmetic properties of group invariants. There are results in the literature determining the structure of finite groups…

A group is called decomposable if it can be expressed as a direct product of two proper subgroups, and indecomposable otherwise. This paper explores the decomposability of virtual Artin groups, which were introduced by Bellingeri, Paris,…

This work presents an approach towards the representation theory of the braid groups $B_n$. We focus on finite-dimensional representations over the field of Laurent series which can be obtained from representations of infinitesimal braids,…

We show that a relatively hyperbolic group either is virtually cyclic or has uniform exponential growth.

We exhibit infinite, solvable, virtually abelian groups with a fixed number of generators, having arbitrarily large balls consisting of torsion elements. We also provide a sequence of 3-generator non-virtually nilpotent polycyclic groups of…

It is well-known that special 2-groups can be described in terms of quadratic maps over fields of characteristic 2. In this article we develop methods to compute conjugacy classes, complex representations and characters of a real special…

We prove that the virtual cactus group has a finite index subgroup that is the fundamental group of a compact special cube complex.

We characterize relatively hyperbolic groups whose reduced $C^*$-algebra is simple as those, which have no non-trivial finite normal subgroups.

We show that a countable group is locally virtually cyclic if and only if its Bredon cohomological dimension for the family of virtually cyclic subgroups is at most one.