Related papers: Some open problems on Coxeter groups and unimodali…

We study structures of derivation modules of Coxeter multiarrangements with quasi-constant multiplicities by using the primitive derivation. As an application, we show that the characteristic polynomial of a Coxeter multiarrangement with…

Several results about the union-closed sets conjecture are presented.

In this note, we give a remark on the structure of centralizers of involutions in Coxeter groups.

We point out four problems which have arisen during the recent research in the domain of Combinatorial Physics.

Computations in small Coxeter groups or dihedral groups suggest that the partition into Kazhdan-Lusztig cells with unequal parameters should obey to some semicontinuity phenomenon (as the parameters vary). The aim of this paper is to…

This paper contains a selection, dictated by personal taste and by no means complete, of open problems in local discrete holomorphic dynamics.

The paper contains a discussion on a number of open problems in queueing theory. Some of them are known for decades, some are more recent. They relate to stability and to rare events. There is an idea to prepare a special issue of QUESTA on…

In this short note we present some remarks and conjectures on two of Erd\"os's open problems in number theory.

Some of the fundamental notions related to sets of lengths of Krull monoids with finite class group are discussed, and a survey of recent results is given. These include the elasticity and related notions, the set of distances, and the…

We construct a family of right-angled Coxeter groups which provide counter-examples to questions about the stable boundary of a group, one-endedness of quasi-geodesically stable subgroups, and the commensurability types of right-angled…

In this short note we discuss the interplay between finite Coxeter groups and construction of wavelet sets, generalized multiresolution analysis and sampling.

In this paper, we give a characterization of Coxeter group representations of Lusztig's a-function value 1, then determine all the irreducible such representations for certain simply laced Coxeter groups.

This paper gives an introduction to some results on monodromy groupoids and the monodromy principle, and then develops the notion of monodromy groupoid for group groupoids.

In the introduction of this paper we discuss a possible approach to the unitarizability problem for classical p-adic groups. In this paper we give some very limited support that such approach is not without chance. In a forthcoming paper we…

We provide a survey of past research and a list of open problems regarding central simple algebras and the Brauer group over a field, intended both for experts and for beginners.

A survey of problems, conjectures, and theorems about quasi-isometric classification and rigidity for finitely generated solvable groups.

We state a number of open questions on 3-dimensional Poincar\'e duality groups and their subgroups, motivated by considerations from 3-manifold topology.

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…

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…

Recent results on finite open group transformations are reviewed.