Related papers: Higher signs for Coxeter groups

We define the notion of a climbing element in a finite real reflection group relative to a total order on the reflection set and we characterise these elements in the case where the total order arises from a bipartite Coxeter element.

We follow the dual approach to Coxeter systems and show for Weyl groups a criterium which decides whether a set of reflections is generating the group depending on the root and the coroot lattice. Further we study special generating sets…

An axiomatic approach to the representation theory of Coxeter groups and their Hecke algebras was presented in [1]. Combinatorial aspects of this construction are studied in this paper. In particular, the symmetric group case is…

When the standard representation of a crystallographic Coxeter group is reduced modulo an odd prime p, one obtains a finite group G^p acting on some orthogonal space over Z_p . If the Coxeter group has a string diagram, then G^p will often…

We introduce the concept of hyperreflection groups, which are a generalization of Coxeter groups. We prove the Deletion and Exchange Conditions for hyperreflection groups, and we discuss special subgroups and fundamental sectors of…

Graph products of cyclic groups and Coxeter groups are two families of groups that are defined by labeled graphs. The family of Dyer groups contains these both families and gives us a framework to study these groups in a unified way. This…

Coxeter groups are a special class of groups generated by involutions. They play important roles in the various areas of mathematics. This survey particularly focuses on how one uses Coxeter groups to construct interesting examples of…

We construct a nontrivial cyclic cocycle on the Weyl algebra of a symplectic vector space. Using this cyclic cocycle we construct an explicit, local, quasi-isomorphism from the complex of differential forms on a symplectic manifold to the…

We study natural partial normalization spaces of Coxeter arrangements and discriminants and relate their geometry to representation theory. The underlying ring structures arise from Dubrovin's Frobenius manifold structure which is lifted…

We define a generalization of Coxeter graphs and an associated Coxeter system and Coxeter mapping class. These can be used to construct periodic Coxeter mapping classes on surfaces with arbitrarily large genus, preserving lots of…

In a 2015 paper we have defined a map from the set of conjugacy classes in a Weyl group W to the set of irreducible representations of W (its image parametrizes the strata of a reductive group with Weyl group W). In this paper we provide…

Orbits of the Weyl reflection groups attached to the simple Lie groups $A_2, C_2, G_2$ and Coxeter group $H_2$ are considered. For each of the groups products of any two orbits are decomposed into the union of the orbits. Results are…

Mirror graphs were introduced by Bre\v{s}ar et al. in 2004 as an intriguing class of graphs: vertex-transitive, isometrically embeddable into hypercubes, having a strong connection with regular maps and polytope structure. In this article…

We determine a fundamental domain for the diagonal action of a finite Coxeter group $W$ on $V^{\oplus n}$, where $V$ is the reflection representation. This is used to give a stratification of $V^{\oplus n}$, which is respected by the group…

The problem of interpreting a set of ${\cal W}$-algebra constraints constructed in terms of an arbitrarily twisted scalar field as the recursion relations of a topological theory is addressed. In this picture, the conventional models of…

We consider the class of those Coxeter groups for which removing from the Cayley graph any tubular neighbourhood of any wall leaves exactly two connected components. We call these Coxeter groups bipolar. They include both the virtually…

In this paper we introduce the galaxy of Coxeter groups -- an infinite dimensional, locally finite, ranked simplicial complex which captures isomorphisms between Coxeter systems. In doing so, we would like to suggest a new framework to…

Let ${\mathcal A}$ be a finite real linear hyperplane arrangement in three dimensions. Suppose further that all the regions of ${\mathcal A}$ are isometric. We prove that ${\mathcal A}$ is necessarily a Coxeter arrangement. As it is well…

Let W be a finite Coxeter group. We define its Hecke-group algebra by gluing together appropriately its group algebra and its 0-Hecke algebra. We describe in detail this algebra (dimension, several bases, conjectural presentation,…

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