Related papers: Classification of spin-chain braid representations
We classify homomorphisms from the braid group on $n$ strands to the pure mapping class group of a nonoriantable surface of genus $g$. For $n\ge 14$ and $g\le 2\lfloor{n/2}\rfloor+1$ every such homomorphism is either cyclic, or it maps…
A transversal matroid $M$ of rank $r$ on $[n]$ can be associated to a family of binary matrices corresponding to different presentations of $M$. We describe those matrices which arise from unique maximal presentations of size $r$- giving a…
Fragment and glider representations (introduced by F. Caenepeel, S. Nawal, and F. Van Oystaeyen) form a generalization of filtered modules over a filtered ring. Given a $\Gamma$-filtered ring $FR$ and a subset $\Lambda \subseteq \Gamma$, we…
In this paper we derive from arguments of string scattering a set of eight tetrahedron equations, with different index orderings. It is argued that this system of equations is the proper system that represents integrable structures in three…
In this thesis, we develop the theory of bifibrations of polycategories. We start by studying how to express certain categorical structures as universal properties by generalising the shape of morphism. We call this phenomenon…
We set up a fibred categorical theory of obstruction and classification of morphisms that specializes to the one of monoidal functors between categorical groups and also to the Schreier-Mac Lane theory of group extensions. Further…
In this paper we give necessary and sufficient conditions for a functor to be representable in a strongly generated triangulated category which has a linear action by a graded ring, and we discuss some applications and examples.
We study representations of the braid groups from braiding gapped boundaries of Dijkgraaf-Witten theories and their twisted generalizations, which are (twisted) quantum doubled topological orders in two spatial dimensions. We show that the…
We give an alternate conception of string diagrams as labeled 1-dimensional oriented cobordisms, the operad of which we denote by Cob/O, where O is the set of string labels. The axioms of traced (symmetric monoidal) categories are fully…
We prove the theorem stated in the title. More precisely, we show the stronger statement that every symmetric monoidal left adjoint functor between presentably symmetric monoidal infinity-categories is represented by a strong symmetric…
We identify natural symmetries of each rigid higher braided category. Specifically, we construct a functorial action by the continuous group $\Omega \mathsf{O}(n)$ on each $\mathcal{E}_{n-1}$-monoidal $(g,d)$-category $\mathcal{R}$ in which…
A braided $Ann$-category $\mathcal A$ is an $Ann$-category $\mathcal A$ together with a braiding $c$ such that $(\mathcal A, \otimes, a, c, (1,l,r))$ is a braided tensor category, moreover $c$ is compatible with the distributivity…
In particle phenomenology, preon models study compositional rules of standard model interactions. In spite of empirical success, mathematical underpinnings of preon models in terms of group representation theory have not been fully worked…
We establish a braid monodromy representation of functions satisfying an algebraic equation containing three terms (trinomial equation). We follow global analytic continuation of the roots to a trinomial algebraic equation that are…
It is well-known that the Gauss decomposition of the generator matrix in the $R$-matrix presentation of the Yangian in type $A$ yields generators of its Drinfeld presentation. Defining relations between these generators are known in an…
A near-group category is an additively semisimple category with a product such that all but one of the simple objects is invertible. We classify braided structures on near-group categories, and give explicit numerical formulas for their…
In this work, we analyze the structure of the category of partial representations of a finite group $G$ as a multifusion category, providing an alternative way to describe simple objects and their tensor products. We describe the…
This article offers an intuitive introduction to monoidal categories through the lens of painting, presenting abstract mathematical concepts with visual and tactile analogies. Aimed at curious undergraduates and non-specialists, it seeks to…
In this paper, we introduce the definitions of signatures of braided fusion categories, which are proved to be invariants of their Witt equivalence classes. These signature assignments define group homomorphisms on the Witt group. The…
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.