Related papers: Alternating subgroups of Coxeter groups

The Bruhat order on a Coxeter group is often described by examining subexpressions of a reduced expression. We prove that an analogous description applies to the Bruhat order on double cosets. This establishes the compatibility of the…

We study and classify a class of representations (called generalized geometric representations) of a Coxeter group of finite rank. These representations can be viewed as a natural generalization of the geometric representation. The…

We give several algorithms addressing computations of intersections of conjugate subgroups.

In the paper it is proven that Carter subgroups of a finite group are conjugate. A complete classification of Carter subgroups in finite almost simple groups is also obtained.

We investigate the compatibility of the set of fully commutative elements of a Coxeter group with the various types of Kazhdan-Lusztig cells using a canonical basis for a generalized version of the Temperley-Lieb algebra.

We introduce the notion of Rota-Baxter coalgebra which can be viewed as the dual notion of Rota-Baxter algebra. We provide some concrete examples and establish various properties of this new object. We also consider comodules over…

We obtain a description of the irreducible representation algebra of the alternating group of degree four over the ring of 2-adic integers.

The real theory of the Dunkl operators has been developed very extensively, while there still lacks the corresponding complex theory. In this paper we introduce the complex Dunkl operators for certain Coxeter groups. These complex Dunkl…

We discuss combinatorial conditions for the existence of various types of reductions between equivalence relations, and in particular identify necessary and sufficient conditions for the existence of injective reductions.

This is a survey of some aspects of the large-scale geometry of right-angled Coxeter groups. The emphasis is on recent results on their negative curvature properties, boundaries, and their quasi-isometry and commensurability classification.

We study the quiver of the descent algebra of a finite Coxeter group W. The results include a derivation of the quiver of the descent algebra of types A and B. Our approach is to study the descent algebra as an algebra constructed from the…

We examine the partition of a finite Coxeter group of type $B$ into cells determined by a weight function $L$. The main objective of these notes is to reconcile Lusztig's description of constructible representations in this setting with…

A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.

This paper is about a small combinatorial trick, which is well known, but has no name. Let G be a permutation group acting on a vector space M. There is a natural way to assign a cosimplicial space to these data. We call the resulting…

We combinatorially characterize the number $\mathrm{cc}_2$ of conjugacy classes of involutions in any Coxeter group in terms of higher rank odd graphs. This notion naturally generalizes the concept of odd graphs, used previously to count…

We propose various problems about Borel complexity of characterized subgroups of compact abelian groups, inspired by our forthcoming paper \cite{DI3}.

We use covariants of binary sextics to describe the structure of modules of scalar-valued or vector-valued Siegel modular forms of degree 2 with character, over the ring of scalar-valued Siegel modular forms of even weight. For a modular…

In the previous article we introduced the new concept of mixed representations of quivers and described the generators of their algebras of invariants. In this article we describe the defining relations of these algebras. Some applications…

There is a well-known classification of conjugacy classes of involutions in finite Coxeter groups, in terms of subsets of nodes of their Coxeter graphs. In many cases, the product of an involution with the longest element is again an…

We show that the Morse boundary of a right-angled Coxeter group may contain embedded circles that do not arise as the boundary of a Morse Fuchsian subgroup visible in the defining graph.