Related papers: Reflection subgroups of Euclidean reflection group…

Let $O(p,q)$ be the orthogonal groups of signature $(p,q)$ over the reals. It is shown that an element of the commutator subgroup $O(p,q)'$ of $O(p,q)$ is bireflectional (product of 2 involutions in $O(p,q)'$) if and only if it is…

Let W be a finite group generated by unitary reflections and A be the set of reflecting hyperplanes. We will give a characterization of the logarithmic differential forms with poles along A in terms of anti-invariant differential forms. If…

Williamson defined the category of singular Soergel bimodules attached to a reflection faithful representation of a Coxeter group. We generalize this construction to more general realizations of Coxeter groups.

For weighted group convoltion measure algebra we construct a representation on reflexsive space.

Following Vinberg, we find the criterions for a subgroup generated by reflections $\Gamma \subset \SL^{\pm}(n+1,\mathbb{R})$ and its finite-index subgroups to be definable over $\mathbb{A}$ where $\mathbb{A}$ is an integrally closed…

We compute Euler characteristics of p-subgroup categories of finite groups

We study coherence of graph products and Coxeter groups and obtain many results in this direction.

The structure of the coincidence symmetry group of an arbitrary $n$-dimensional lattice in the $n$-dimensional Euclidean space is considered by describing a set of generators. Particular attention is given to the coincidence isometry…

The invariants of finite-dimensional representations of simple Lie algebras, such as even-degree indices and anomaly numbers, are considered in the context of the non-crystallographic finite reflection groups $H_2$, $H_3$ and $H_4$. Using a…

On etudie divers aspects d'une formule qui compte les reflexions pleines dans les groupes de Coxeter finis. ***** We study several points about a formula which counts reflexions in a finite Coxeter group whose reduced decompositions involve…

Shephard groups are unitary reflection groups arising as the symmetries of regular complex polytopes. For a Shephard group, we identify the representation carried by the principal ideal in the coinvariant algebra generated by the image of…

We obtain a number of results regarding freeness, quasiconvexity and separability for subgroups of Coxeter groups, Artin groups and one-relator groups with torsion.

We compute the Hochschild cohomology groups of the cluster-tilted algebras of finite representation type.

This is an overview article on compact Lie groups and their representations, written for the Encyclopedia of Mathematical Physics to be published by Elsevier.

Complex reflection groups of rank two are precisely the finite groups in the family of groups that we call J-reflection groups. These groups are particular cases of J-groups as defined by Achar & Aubert in 2008. The family of J-reflection…

We study Coxeter diagrams of some unitary reflection groups. Using solely the combinatorics of diagrams, we give a new proof of the classification of root lattices defined over $\cE = \ZZ[e^{2 \pi i/3}]$: there are only four such lattices,…

We present an elementary type preserving bijection between noncrossing and nonnesting partitions for all classical reflection groups, answering a question of Athanasiadis.

In this paper I present some open problems on Coxeter groups and unimodality, together with the main partial results, and computational evidence, that are known about them.

The present article gives the index formula of the principal congruence subgroups of the Hecke group H_5

In this note, we give a remark on the structure of centralizers of involutions in Coxeter groups.