Related papers: Braids inside the Birman-Wenzl-Murakami algebra

We prove a degree-one saving bound for the dimension of the space of cohomological automorphic forms of fixed level and growing weight on $\mathrm{SL}_2$ over any number field that is not totally real. In particular, we establish a sharp…

Let $X=\C^n$. In this paper we present an algorithm that computes the de Rham cohomology groups $H^i_{dR}(U,\C)$ where $U$ is the complement of an arbitrary Zariski-closed set $Y$ in $X$. Our algorithm is a merger of the algorithm given by…

We study the Zariski topology of the ind-groups of polynomial and free associative algebras $\Aut(K[x_1,...,x_n])$ (which is equivalent to the automorphism group of the affine space $\Aut(K^n))$) and $\Aut(K< x_1,..., x_n>$ via…

Let $\mathbf{k}$ be an algebraically closed field. Recently, K. Erdmann classified the symmetric $\mathbf{k}$-algebras $\Lambda$ of finite representation type such that every non-projective module $M$ has period dividing four. The goal of…

In this paper we prove that for any connected reductive algebraic group G and a large enough prime $l$, there are continuous homomorphisms $$\mathrm{Gal}(\bar\mathbb Q/\mathbb Q) \to G(\bar\mathbb Q_l)$$ with Zariski-dense image, in…

We define a class of monoidal categories whose morphisms are diagrams, and which are enhancements and generalisations of the Brauer category obtained by adjoining infinitesimal braids, "coupons" and poles. Properties of these categories are…

In this paper, complement-equivalent arithmetic Zariski pairs will be exhibited answering in the negative a question by Eyral-Oka on these curves and their groups. A complement-equivalent arithmetic Zariski pair is a pair of complex…

We factorize 4d Fradkin-Linetsky higher spin conformal algebra by maximal ideal $I^1-\alpha$ and construct irreducible infinite-dimensional modules $M_\alpha$ of 4d conformal algebra that are parameterized by real number $\alpha$. It is…

We show that any twisted Dijkgraaf-Witten representation of a mapping class group of an orientable, compact surface with boundary has finite image. This generalizes work of Etingof, Rowell and Witherspoon showing that the braid group images…

We show that every Lie algebra or superLie algebra has a canonical braiding on it, and that in terms of this its enveloping algebra appears as a flat space with braided-commuting coordinate functions. This also gives a new point of view…

A construction of bases for cell modules of the Birman--Murakami--Wenzl (or B--M--W) algebra $B_n(q,r)$ by lifting bases for cell modules of $B_{n-1}(q,r)$ is given. By iterating this procedure, we produce cellular bases for B--M--W…

The disjoint union of mapping class groups of surfaces forms a braided monoidal category $\mathcal M$, as the disjoint union of the braid groups $\mathcal B$ does. We give a concrete, and geometric meaning of the braiding $\beta_{r,s}$ in…

We show that the Lawrence-Krammer representation based on two parameters that was used by Bigelow and independently Krammer to show the linearity of the braid group is generically irreducible, but that when its parameters are specialized to…

Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field. Criteria are given which characterize existence of a fine or coarse moduli space classifying, up to isomorphism, the representations of $\Lambda$ with fixed…

We address the question of finding algebraic properties that are respectively equivalent, for a morphism between algebraic varieties over an algebraically closed field of characteristic zero, to be an homeomorphism for the Zariski topology…

Two series of W-algebras with two generators are constructed from chiral vertex operators of a free field representation. If $c = 1 - 24k$, there exists a W(2,3k) algebra for k in $Z_{+}/2$ and a W(2,8k) algebra for k in $Z_{+}/4$. All…

We establish a connection between certain unique models, or equivalently unique functionals, for representations of p-adic groups and linear characters of their corresponding Hecke algebras. This allows us to give a uniform evaluation of…

In this paper we study spaces of algebras over an operad (non-symmetric) in symmetric monoidal model categories. We first compute the homotopy fiber of the forgetful functor sending an algebra to its underlying object, extending a result of…

Let $(\mathcal{G},\nu)$ be a $t$-discrete ergodic groupoid. Consider a finite Von Neumann algebra $\mathcal{M}$ with separable predual. We prove that every uniformly bounded measurable representation $\rho:\mathcal{G} \rightarrow…

We compute explicitly the monodromy representations of "cyclotomic" analogs of the Knizhnik--Zamolodchikov differential system. These are representations of the type B braid group $B_n^1$. We show how the representations of the braid group…