Related papers: Higher signs for Coxeter groups

In this paper, we generalize Serre's splitting theorem for cohomological invariants of the symmetric group to finite Coxeter groups, provided that the ground field has characteristic zero. We then use this principle to determine all the…

We give a monoidal presentation of Coxeter and braid 2-groups, in terms of decorated planar graphs. This presentation extends the Coxeter presentation. We deduce a simple criterion for a Coxeter group or braid group to act on a category.

We represent the rational and mod $p$ cohomology groups of classifying spaces of rank 3 Kac-Moody groups by a direct sum of the invariants of Weyl groups and their quotients. As an application, the authors conclude that there is a…

We define the Coxeter cochain complex of a Coxeter group (G,S) with coefficients in a Z[G]-module A. This is closely related to the complex of simplicial cochains on the abstract simplicial complex I(S) of the commuting subsets of S. We…

We use probabilistic methods to prove that many Coxeter groups are incoherent. In particular, this holds for Coxeter groups of uniform exponent > 2 with sufficiently many generators.

Affine Coxeter groups are fundamental objects in mathematics and in crystallography. If two group elements are conjugate, then they have very similar algebraic and geometric properties. Using recent structural results of Mili\'cevi\'c,…

Soergel bimodule category B is a categorification of the Hecke algebra of a Coxeter system (W,S). We find a presentation of B (as a tensor category) by generators and relations when W is a right-angled Coxeter group.

The descent algebra of a finite Coxeter group $W$ is a basic algebra, and as such it has a presentation as quiver with relations. In recent work, we have developed a combinatorial framework which allows us to systematically compute such a…

For a Coxeter group $W$ we have an associating bi-linear form $B$ on suitable real vector space. We assume that $B$ has the signature $(n-1,1)$ and all the bi-linear form associating rank $n' (\ge 3)$ Coxeter subgroups generated by subsets…

After classifying 3-dimensional hyperbolic Coxeter pyramids by means of elementary plane geometry, we calculate growth functions of corresponding Coxeter groups by using Steinberg formula and conclude that growth rates of them are always…

Tetrahedron equation is a three dimensional analogue of the Yang-Baxter equation. It allows a formulation in terms of the Coxeter group $A_3$. This short note includes miscellaneous remarks on the generalizations along $B_3, C_3, F_4$ and…

Certain results on representations of quivers have analogs in the structure theory of general Coxeter groups. A fixed Coxeter element turns the Coxeter graph into an acyclic quiver, allowing for the definition of a preprojective root. A…

In this note we first consider a ternary matrix group related to the von Neumann regular semigroups and to the Artin braid group (in an algebraic way). The product of a special kind of ternary matrices (idempotent and of finite order)…

It is proposed that instead of normal representations one should look at cocycles of group extensions valued in certain groups of unitary operators acting in a Hilbert space (e.g the Fock space of chiral fermions), when dealing with groups…

We define a subset of the set of special representations of a Weyl group. This subset contains at most one representation.

Given an irreducible well-generated complex reflection group W with Coxeter number h, we call a Coxeter element any regular element (in the sense of Springer) of order h in W; this is a slight extension of the most common notion of Coxeter…

A Coxeter group admits infinite-dimensional irreducible complex representations if and only if it is not finite or affine. In this paper, we provide a construction of some of those representations for certain Coxeter groups using some…

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.

A cohomology theory of weighted Rota-Baxter $3$-Lie algebras is introduced. Formal deformations, abelian extensions, skeletal weighted Rota-Baxter $3$-Lie 2-algebras and crossed modules of weighted Rota-Baxter 3-Lie algebras are interpreted…

We show how Coxeter's work implies a bijection between complex reflection groups of rank two and real reflection groups in $O(3)$. We also consider this magic square of reflections and rotations in the framework of Clifford algebras: we…