Related papers: Modular framization of the BMW algebra

We investigate involutive, non-combinatorial solutions of the braid equation viewed as special deformations of the permutation map. By employing these solutions, we identify the associated quantum algebra, which we introduce as the…

The infinite series of logarithmic minimal models LM(1,p) is considered in the W-extended picture where they are denoted by WLM(1,p). As in the rational models, the fusion algebra of WLM(1,p) is described by a simple graph fusion algebra.…

Matrix-valued holomorphic quantum modular forms are intricate objects that arise in successive refinements of the Volume Conjecture of knots and involve three holomorphic, asymptotic and arithmetic objects. It is expected that the algebraic…

We model proteins with intramolecular bonds, such as disulfide bridges, using the concept of bonded knots -- closed loops in three-dimensional space equipped with additional bonds that connect different segments of the knot. We extend the…

In this paper we first present the construction of the new 2-variable classical link invariants arising from the Yokonuma-Hecke algebras ${\rm Y}_{d,n}(q)$, which are not topologically equivalent to the Homflypt polynomial. We then present…

A representation of the Birman-Wenzl-Murakami algebra BW_{t}(-q^{2n},q) exists in the centraliser algebra End_{U_q(osp(1|2n))}(V^{\otimes t}), where V is the fundamental (2n+1)-dimensional irreducible U_{q}(osp(1|2n))-module. This…

We prove that the 2-variable BMW algebra embeds into an algebra constructed from the HOMFLY-PT polynomial. We also prove that the so(2N)-BMW algebra embeds in the q-Schur algebra of type A. We use these results to construct…

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…

We extend knot contact homology to a theory over the ring $\mathbb{Z}[\lambda^{\pm 1},\mu^{\pm 1}]$, with the invariant given topologically and combinatorially. The improved invariant, which is defined for framed knots in $S^3$ and can be…

A connection is made between the Krammer representation and the Birman-Murakami-Wenzl algebra. Inspired by a dimension argument, a basis is found for a certain irrep of the algebra, and relations which generate the matrices are found.…

This paper introduces an algebra structure on the part of the skein module of an arbitrary $3$-manifold $M$ spanned by links that represent $0$ in $H_1(M;\mathbb{Z}_2)$ when the value of the parameter used in the Kauffman bracket skein…

We construct new solvable vertex models based on the spin representation of the Lie algebra $B_k$. We use these models to study the algebraic structure underlying such vertex theories. We show that all the $B_k$ spin vertex models obey a…

In this paper we represent the classical braids in the Yokonuma--Hecke and the adelic Yokonuma--Hecke algebras. More precisely, we define the completion of the framed braid group and we introduce the adelic Yokonuma--Hecke algebras, in…

This work identifies the Reshetikhin-Turaev invariant of links in terms of a trace map on factorization homology. In particular, to recover the knot invariants associated to Chern-Simons theories, we construct a filtered…

In the continuity of our previous paper arXiv:1509.05516, we define three new algebras, $A_{n}(a,b,c)$, $B_{n}$ and $C_{n}$, that are close to the braid algebra. They allow to build solutions to the braided Yang-Baxter equation with…

We consider a type III subfactor $N\subset M$ of finite index with a finite system of braided $N$-$N$ morphisms which includes the irreducible constituents of the dual canonical endomorphism. We apply $\alpha$-induction and, developing…

We study representation theory of Drinfel'd twists, in terms of what we call F matrices, associated to finite dimensional irreducible modules of quantum affine algebras, and which factorize the corresponding (unitary) R matrices. We…

In this lecture we explain the intimate relationship between modular invariants in conformal field theory and braided subfactors in operator algebras. Our analysis is based on an approach to modular invariants using braided sector induction…

For the quantum walled Brauer algebra, we construct its Specht modules and (for generic parameters of the algebra) seminormal modules. The latter construction yields the spectrum of a commuting family of Jucys--Murphy elements. We also…

We initiate a general approach to the relative braid group symmetries on (universal) $\imath$quantum groups, arising from quantum symmetric pairs of arbitrary finite types, and their modules. Our approach is built on new intertwining…