Related papers: Monodromy Representations of Mixed Braid Groups

Let B be the generalized braid group associated to some finite complex reflection group. We define a representation of B of dimension the number of reflections of the corresponding reflection group, which generalizes the Krammer…

In this article, we introduce the notion of representations of polyadic groups and we investigate the connection between these representations and those of retract groups and covering groups.

Consider the ring R:=\Q[\tau,\tau^{-1}] of Laurent polynomials in the variable \tau. The Artin's Pure Braid Groups (or Generalized Pure Braid Groups) act over R, where the action of every standard generator is the multiplication by \tau. In…

The purpose of this article is to describe the integral cohomology of the braid group B_3 and SL_2(Z) with local coefficients in a classical geometric representation given by symmetric powers of the natural symplectic representation. These…

We prove that braid group representations associated to braided fusion categories and mapping class group representations associated to modular fusion categories are always semisimple. The proof relies on the theory of extensions in…

Given a representation $\varphi \colon B_n \to G_n$ of the braid group $B_n$, $n \geq 2$ into a group $G_n$, we are considering the problem of whether it is possible to extend this representation to a representation $\Phi \colon SM_n \to…

We prove that representations of the braid groups coming from weakly group-theoretical braided fusion categories have finite images.

In this paper the author finds explicitly all finite-dimensional irreducible representations of a series of finite permutation groups that are homomorphic images of Artin braid group.

To a univariate monic polynomial is attached a special planar forest that is called the picture of the polynomial. Isotopy classes of pictures are called signatures. All combinatorially possible signatures are realized and spaces of…

We investigate the braid group representations arising from categories of representations of twisted quantum doubles of finite groups. For these categories, we show that the resulting braid group representations always factor through finite…

Using a unified method, we determine the structure of automorphisms and representations of arbitrary polyadic groups. More precisely, for a polyadic group $(G, f)=der_{\theta, b}(G, \cdot)$, we obtain a complete description of automorphisms…

This paper is devoted to the proof of a structural theorem, concerning certain homomorphic images of Artin braid group on $n$ strands in finite symmetric groups. It is shown that any one of these permutation groups is an extension of the…

We express the cohomology of the basic stratum of some unitary Shimura varieties associated to division algebras in terms of automorphic representations of the group in the Shimura datum.

By studying braid group actions on Milnor's construction of the 1-sphere, we show that the general higher homotopy group of the 3-sphere is the fixed set of the pure braid group action on certain combinatorially described group. We also…

In this paper we introduce a strict monoidal subcategory of the category of matrices, suitable to address a higher representation theoretic analogue of radicals (non-semisimplicity) in ordinary representation theory. We show the extent to…

We use a geometric approach to show that the reduced Burau representation specialized at roots of unity has another incarnation as the monodromy representation of a moduli space of Euclidean cone metrics on the sphere, as described by…

Given a group $G$ of automorphisms of a matroid $M$, we describe the representations of $G$ on the homology of the independence complex of the dual matroid $M^*$. These representations are related with the homology of the lattice of flats…

We express the hairy graph complexes computing the rational homotopy groups of long embeddings (modulo immersion) of R^m in R^n as "decorated" graph complexes associated to certain representations of the outer automorphism groups of free…

This article gives certain fibre bundles associated to the braid groups which are obtained from a translation as well as conjugation on the complex plane. The local coefficient systems on the level of homology for these bundles are given in…

We relate endotrivial representations of a finite group in characteristic p to equivariant line bundles on the simplicial complex of non-trivial p-subgroups, by means of weak homomorphisms.