Related papers: Fully commutative elements of the complex reflecti…
For Coxeter groups with sufficiently large braid relations, we prove that the sequence of powers of a Coxeter element has unbounded reflection length. We establish a connection between the reflection length functions on arbitrary Coxeter…
In this work we study representations of certain Coxeter groups to obtain some properties of the corresponding reflection groups.
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…
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…
Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$. In this paper, we first introduce and study the notions of $s$-pure exact sequences and $s$-absolutely pure modules which extend the classical notions of…
It is shown that, under mild conditions, a complex reflection group $G(r,p,n)$ may be decomposed into a set-wise direct product of cyclic subgroups. This property is then used to extend the notion of major index and a corresponding Hilbert…
In Finite Group Modular Representation Theory, the basic objects are the indecomposable and simple modules. This paper offers a new classification of these objects that refines the Green Theory Classification of indecomposable and simple…
A totally symmetric set is a finite subset of a group for which any permutation of the elements can be realized by conjugation in the ambient group. Such sets are rigid under homomorphisms, and so exert a great deal of control over the…
We give a new characterization of partial groups as a subcategory of symmetric (simplicial) sets. This subcategory has an explicit reflection, which permits one to compute colimits in the category of partial groups. We also introduce the…
For every dimension d, there is an infinite family of convex co-compact reflection groups of isometries of hyperbolic d-space --- the superideal (simplicial and cubical) reflection groups --- with the property that a random group at any…
Recall that an element $x\in R$ is {\bf complemented} if there is a $y\in R$ such that $xy = 0$ and $x + y \in {\rm reg}(R)$. In a recent article [1], the authors investigated those rings for which every non-nilpotent element is…
This paper is an attempt to find out which properties of a finite group G can be expressed in terms of commutators of elements of coprime orders. A criterion of solubility of G in terms of such commutators is obtained. We also conjecture…
For every imprimitive complex reflection group of rank 2, we construct a semi-orthogonal decomposition of the derived category of the associated global quotient stack which categorifies the usual decomposition of the orbifold cohomology…
Various descending chains of subgroups of a finite permutation group can be used to define a sequence of `basic' permutation groups that are analogues of composition factors for abstract finite groups. Primitive groups have been the…
We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…
We consider indecomposable representations of the Klein four group over a field of characteristic $2$ and of a cyclic group of order $pm$ with $p,m$ coprime over a field of characteristic $p$. For each representation we explicitly describe…
All possible products of all elements of an odd order finite group are considered. A set of all such products is called as a K-set. A hypothesis of K-set coincidence of any group of an odd order with its commutant is proposed and the…
We introduce Coxeter-sortable elements of a Coxeter group W. For finite W, we give bijective proofs that Coxeter-sortable elements are equinumerous with clusters and with noncrossing partitions. We characterize Coxeter-sortable elements in…
In this paper we classify reflection subgroups of Euclidean Coxeter groups.
We formulate and prove relative versions of several classical decompositions known in the theory of Chevalley groups over commutative rings. As an application we obtain upper estimates for the width of principal congruence subgroups in…