Related papers: Nonabelian braid statistics versus projective perm…

The Weil representation of the symplectic group associated to a finite abelian group of odd order is shown to have a multiplicity-free decomposition. When the abelian group is p-primary, the irreducible representations occurring in the Weil…

The necklace braid group $\mathcal{NB}_n$ is the motion group of the $n+1$ component necklace link $\mathcal{L}_n$ in Euclidean $\mathbb{R}^3$. Here $\mathcal{L}_n$ consists of $n$ pairwise unlinked Euclidean circles each linked to an…

We prove the spin-statistics theorem for massive particles obeying braid group statistics in three-dimensional Minkowski space. We start from first principles of local relativistic quantum theory. The only assumption is a gap in the mass…

Quantum computers provide a super-exponential speedup for performing a Fourier transform over the symmetric group, an ability for which practical use cases have remained elusive so far. In this work, we leverage this ability to unlock…

In this paper we indicate one method of construction of linear representations of groups and algebras with translation invariant (except, maybe , finite number) defining relationships. As an illustration of this method, we give one approach…

In the recent paper [AF12], we introduced an analysis of the Brylinski-Kostant model for spherical minimal representations for simple real Lie groups of non Hermitian type. We generalize here that analysis and give a unified geometric…

Braided quantum field theories proposed by Oeckl can provide a framework for defining quantum field theories having Hopf algebra symmetries. In quantum field theories, symmetries lead to non-perturbative relations among correlation…

By considering `coloured' braid group representation we have obtained a quantum group, which reduces to the standard $GL_q(2)$ and $GL_{p,q}(2)$ cases at some particular limits of the `colour' parameters. In spite of quite complicated…

Permutation and its partial transpose play important roles in quantum information theory. The Werner state is recognized as a rational solution of the Yang--Baxter equation, and the isotropic state with an adjustable parameter is found to…

Indistinguishability of particles is a fundamental principle of quantum mechanics. For all elementary and quasiparticles observed to date - including fermions, bosons, and Abelian anyons - this principle guarantees that the braiding of…

We study projective unitary (co)representations of compact quantum groups and the associated second cohomology theory. We introduce left/right/bi/strongly projective corepresentations and study them in details. In particular, we prove that…

Braided groups and braided matrices are novel algebraic structures living in braided or quasitensor categories. As such they are a generalization of super-groups and super-matrices to the case of braid statistics. Here we construct braided…

Let ${\mathcal O}$ be an involutive discrete valuation ring with residue field of characteristic not 2. Let $A$ be a quotient of ${\mathcal O}$ by a nonzero power of its maximal ideal and let $*$ be the involution that $A$ inherits from…

Anyons obeying fractional exchange statistics arise naturally in two dimensions: hard-core two-body constraints make the configuration space of particles not simply-connected. The braid group describes how topologically-inequivalent…

We formulate scalar field theories in a curved braided $L_\infty$-algebra formalism and analyse their correlation functions using Batalin-Vilkovisky quantization. We perform detailed calculations in cubic braided scalar field theory up to…

We construct a [(n+1)/2]+1 parameters family of irreducible representations of the Braid group B_3 in arbitrary dimension n\in N, using a q-deformation of the Pascal triangle. This construction extends in particular results by S.P.Humphries…

This paper classifies complex homogeneous $2$-local representations of the multiple virtual braid group $M_kVB_n$ into $\mathrm{GL}_n(\mathbb{C})$ for $n\geq3$ and $k >1$, showing that such representations fall into exactly $2^{k+1}+1$…

We show that representations of the loop braid group arise from Aharonov-Bohm like effects in finite 2-group (3+1)-dimensional topological higher gauge theory. For this we introduce a minimal categorification of biracks, which we call…

It is known that the Lawrence-Krammer representation of the Artin group of type $A_{n-1}$ based on the two parameters $t$ and $q$ that was used by Krammer and independently by Bigelow to show the linearity of the braid group on $n$ strands…

A Haag-Ruelle scattering theory for particles with braid group statistics is developed, and the arising structure of the Hilbert space of multiparticle states is analyzed.