Related papers: A Unified Construction of Coxeter Group Representa…

We use model theoretic techniques to construct explicit first-order axiomatizations for the classes of posets that can be represented as systems of sets, where the order relation is given by inclusion, and existing meets and joins of…

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 introduce a generalization of representations of quivers that contains also representations of posets, vectorspace problems and other matrix problems. Many examples, some of which are given in the paper, show that the language of marked…

By a recent result obtained by R. Howlett and the author considerable progress has been made towards a complete solution of the isomorphism problem for Coxeter groups. In this paper we give a survey on the isomorphism problem and explain in…

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.

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.

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…

These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they have a minimum of prerequisites. Topics include definitions…

We introduce and study functorial and combinatorial constructions concerning equivariant Burnside groups.

We study combinatorial properties of the alternating subgroup of a Coxeter group, using a presentation of it due to Bourbaki.

Let (G,S) be a Coxeter group. We construct a continuation, to the open unit disc, of the unitary representations associated to the positive definite functions g -> r^l(g). (Here 0<r<1, and l denotes the length function with respect to the…

In this paper, we give the enumeration of z-classes in finite Coxeter groups.

We give a brief introduction to the notion of an 'approximate group' and some of its numerous applications.

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…

The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…

We survey the theory of Hitchin representations of Fuchsian groups and describe a conjectural geometric picture of an augmented Hitchin component.

We give a case-by-case description of the centralizers of involutions in finite Coxeter groups.

We calculate extensions between certain irreducible admissible representations of p-adic groups.

The classification of the representations of the generalized deformed oscillator algebra is given together with several comments about possibility of introducing a coproduct structure in some type of deformed oscillator algebra.

In this paper, first we give the notion of a representation of a relative Rota-Baxter Lie algebra and introduce the cohomologies of a relative Rota-Baxter Lie algebra with coefficients in a representation. Then we classify abelian…