Higher Dimensional Irreducible Representations of the Pure Braid Group

Quantum Teichmüller Theory and Representations of the Pure Braid Group

We adapt some of the methods of quantum Teichmüller theory to construct a family of representations of the pure braid group of the sphere. This article presents a variation of the constructions of [2, 3] on the finite-dimensional representation theory of the quantum Teichmüller space. In these two earlier articles, the author and his collaborators considered the quantum Teichmüller space T S of...

Derivative Varieties and the Pure Braid Group

Geometric Presentations for the Pure Braid Group

We give several new positive finite presentations for the pure braid group that are easy to remember and simple in form. All of our presentations involve a metric on the punctured disc so that the punctures are arranged “convexly”, which is why we describe them as geometric presentations. Motivated by a presentation for the full braid group that we call the “rotation presentation”, we introduce...

New Permutation Representations of The Braid Group

We give a new infinite family of group homomorphisms from the braid group Bk to the symmetric group Smk for all k and m ≥ 2. Most known permutation representations of braids are included in this family. We prove that the homomorphisms in this family are non-cyclic and transitive. For any divisor l of m, 1 ≤ l < m, we prove in particular that if m l is odd then there are 1+ m l non-conjugate hom...

Determination of subrepresentations of the standard higher dimensional shearlet group

‎This paper is devoted to definition standard higher dimension shearlet group $ mathbb{S} = mathbb{R}^{+} times mathbb {R}^{n-1} times mathbb {R}^{n} $ and determination of square integrable subrepresentations of this group‎. ‎Also we give a characterisation of admissible vectors associated to the Hilbert spaces corresponding to each su brepresentations‎.