Related papers: Unitary Braid Representations with Finite Image

We begin a systematic study of unitary representations of minimal $W$-algebras. In particular, we classify unitary minimal $W$-algebras and make substantial progress in classification of their unitary irreducible highest weight modules. We…

For abelian length categories the borderline between finite and infinite representation type is discussed. Characterisations of finite representation type are extended to length categories of infinite height, and the minimal length…

We determine the Zariski closure of the representations of the braid groups that factorize through the Birman-Wenzl-Murakami algebra, for generic values of the parameters $\alpha,s$. For $\alpha,s$ of modulus 1 and close to 1, we prove that…

We study and give examples of braided groupoids, and, a fortiori, non-degenerate solutions of the quiver-theoretical braid equation.

We consider birack and switch colorings of braids. We define a switch structure on the set of permutation representations of the braid group and consider when such a representation is a switch automorphism. We define quiver-valued…

We give a finite presentation of the mapping class group of an oriented (possibly bounded) surface of genus greater or equal than 1, considering Dehn twists on a very simple set of curves.

In this paper we explicitly compute finite bases of disjunctive identities and finite bases of regular representations for a number of interesting finite groups.

The purpose of this paper is to describe the images of multilinear polynomials of arbitrary degree on the strictly upper triangular matrix algebra.

We present a proof of an upper bound for the lengths of finite dimensional representations of algebras obeying a modified PBW property, including Lie algebras and quantum groups. The sharpness of the bound is proved and discussed.

We classify the finite-dimensional irreducible linear representations of the Baumslag-Solitar groups BS(p,q) = < a, b | a b^p = b^q a > for relatively prime p and q. The general strategy of the argument is to consider the matrix group given…

The problem of classifying all unitary R-matrices of arbitrary finite dimension that have precisely two distinct eigenvalues is described, working up to a natural equivalence relation given by the characters of their braid group…

By evaluating the Burau representation at t=-1, we obtain a symplectic representation of the braid group. We define the congruence subgroups of the braid group to be the preimages of the principal congruence subgroups of the symplectic…

We prove using a novel random matrix model that all right-angled Artin groups have a sequence of finite dimensional unitary representations that strongly converge to the regular representation. We deduce that this result applies also to:…

By analyzing known presentations of the pure mapping groups of orientable surfaces of genus $g$ with $b$ boundary components and $n$ punctures, we show that these groups are isomorphic to some groups related to the braid groups and the…

We study the TQFT mapping class group representations for surfaces with boundary associated with the $SU(2)$ gauge group, or equivalently the quantum group $U_q(\Sl(2))$. We show that at a prime root of unity, these representations are all…

Given an oriented surface of positive genus with finitely many punctures, we classify the finite orbits of the mapping class group action on the moduli space of semisimple complex special linear two dimensional representations of the…

The classical construction of representations of quivers enables us to consider linear maps between several vector spaces. The mixed representations of quivers helps us to work with linear maps as well as bilinear forms on several vector…

Some of the most classically relevant Hyperplane arrangements are the Braid Arrangements $B_n$ and their associated compliment spaces $\mathcal{F}_n$. In their recent work, Tsilevich, Vershik, and Yuzvinsky construct what they refer to as…

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 consider braids on $m+n$ strands, such that the first $m$ strands are trivially fixed. We denote the set of all such braids by $B_{m,n}$. Via concatenation $B_{m,n}$ acquires a group structure. The objective of this paper is to find a…