Related papers: A Unified Construction of Coxeter Group Representa…

In this paper, we count factorizations of Coxeter elements in well-generated complex reflection groups into products of reflections. We obtain a simple product formula for the exponential generating function of such factorizations, which is…

We compute the Hochschild cohomology groups of the cluster-tilted algebras of finite representation type.

The corepresentation theory of continuous groups is presented without the assumption that the subgroup $G$ of the group with antilinear operations is unitary. The formulas of the corepresentation theory with unitary groups $G$ can be…

In this article, we introduce rotation groups as a common generalisation of Coxeter groups and graph products of groups (including right-angled Artin groups). We characterise algebraically these groups by presentations (periagroups) and we…

A general method for calculating or constructing lower central factors of groups is presented. {\it Relative basic commutators} are defined.

Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…

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…

Coxeter groups are a special class of groups generated by involutions. They play important roles in the various areas of mathematics. This survey particularly focuses on how one uses Coxeter groups to construct interesting examples of…

We introduce an elementary argument to the theory of distribution of sequences modulo one.

We develop a cohomological method to classify amalgams of groups. We generalize this to simplicial amalgams in any concrete category. We compute the non-commutative 1-cohomology for several examples of amalgams defined over small simplices.

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

A monoid structure on families of representations of a quiver is introduced by taking extensions of representations in families, i.e. subvarieties of the varieties of representations. The study of this monoid leads to interesting…

We define and study cocycles on a Coxeter group in each degree generalizing the sign function. When the Coxeter group is a Weyl group, we explain how the degree three cocycle arises naturally from geometry representation theory.

This short note contains elementary evaluations of some Euler sums.

We study finite dimensional representations of the projective modular group. Various explicit dimension formulas are given.

This paper considers a smaller version of the 26-node presentation of the Bimonster group.

We apply the techniques of symmetric generation to establish the standard presentations of the finite simply laced irreducible finite Coxeter groups, that is the Coxeter groups of types An, Dn and En, and show that these are naturally…

An algebraic deformation theory of coalgebra morphisms is constructed.

This paper presents the square integrable representations of generalized Weyl-Heisenberg group. We investigate the quasi regular representation of generalized Weyl-Heisenberg group. Moreover, we obtain a concrete from for admissible vector…

This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection…