Related papers: Coxeter Groups, Wavelets, Multiresolution and Samp…
In a recent paper, Barot and Marsh presented an explicit construction of presentation of a finite Weyl group by any seed of corresponding cluster algebra, i.e. by any diagram mutation-equivalent to an orientation of a Dynkin diagram with…
We give a case-by-case description of the centralizers of involutions in finite Coxeter groups.
In this paper we study the commensurability of hyperbolic Coxeter groups of finite covolume, providing three necessary conditions for commensurability. Moreover we tackle different topics around the field of definition of a hyperbolic…
We introduce the notion of weighted Coxeter graph and associate to it a certain generalization of the standard geometric representation of a Coxeter group. We prove sufficient conditions for faithfulness and non-faithfulness of such a…
This article reviews recent developments in multiresolution analysis which make it a powerful tool for the systematic treatment of the multiple length-scales inherent in the electronic structure of matter. Although the article focuses on…
The class of generalized shearlet dilation groups has recently been developed to allow the unified treatment of various shearlet groups and associated shearlet transforms that had previously been studied on a case-by-case basis. We consider…
We provide involutory symmetric generating sets of finitely generated Coxeter groups, fulfilling a suitable finiteness condition, which in particular is fulfilled in the finite, affine and compact hyperbolic cases.
The notion of wavelets is defined. It is briefly described {\it what} are wavelets, {\it how} to use them, {\it when} we do need them, {\it why} they are preferred and {\it where} they have been applied. Then one proceeds to the…
An elementary approach to the construction of Coxeter group representations is presented.
In this paper, we study the twist-conjecture for Coxeter systems and rigidity of Coxeter systems up to finite twists. For Coxeter systems $(W,R)$ and $(W,S)$, under the untangle-condition for conjugate subsets, we investigate separations…
Samplets are data adapted multiresolution analyses of localized discrete signed measures. They can be constructed on scattered data sites in arbitrary dimension such that they exhibit vanishing moments with respect to any prescribed set of…
A Coxeter system is an ordered pair (W,S) where S is the generating set in a particular type of presentation for the Coxeter group W. A subgroup of W is called special if it is generated by a subset of S. Amalgamated product decompositions…
Coxeter polynomials are important homological invariants that are defined for a large class of finite-dimensional algebras. It is of particular interest to develop methods to compute these polynomials. We define the notion of insertion of a…
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.
In this note, we give a remark on the structure of centralizers of involutions in Coxeter groups.
Wavelet sets that are finite unions of convex sets are constructed in $\mathbb R^n$, $n\geq 2$, for dilation by any expansive matrix that has a power equal to a scalar times the identity and also has all singular values greater than $\sqrt…
These notes give a short introduction to finite Coxeter groups, their classification, and some parts of their representation theory, with a focus on the infinite families. They are based on lectures delivered by the author at the…
A connection between real poles of the growth functions for Coxeter groups acting on hyperbolic space of dimensions three and greater and algebraic integers is investigated. In particular, a geometric convergence of fundamental domains for…
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…
This note introduces a new family of wavelets and a multiresolution analysis, which exploits the relationship between analysing filters and Floquet's solution of Mathieu differential equations. The transfer function of both the detail and…