Related papers: The 4--CB Algebra and Solvable Lattice Models
In this work we introduce the concept of Modular Framization or simply Framization. We construct a framization $F_{d,n}$ of the Birman--Wenzl--Murakami algebra, also known as BMW algebra, and start a systematic study of this framization. We…
We study the connection between Rational Conformal Field Theory (RCFT), $N=2$ massive supersymmetric field theory, and solvable Interaction Round the Face (IRF) lattice models. Specifically, one identifies the fusion rings with the chiral…
The cyclotomic Birman-Wenzl-Murakami algebras are quotients of the affine BMW algebras in which the affine generator satisfies a polynomial relation. We show that the cyclotomic BMW algebras are free modules over any (admissible, integral)…
We complete the classification of $4\times 4$ regular solutions of the Yang-Baxter equation. Apart from previously known models, we find four new models of non-difference form. All the new models give rise to Hamiltonians and transfer…
We establish isomorphisms between certain specializations of Birman-Murakami-Wenzl algebras and the symmetric squares of Temperley-Lieb algebras. These isomorphisms imply a link-polynomial identity due to W. B. R. Lickorish. As an…
The cyclotomic Birman-Murakami-Wenzl (BMW) algebras B_n^k, introduced by R. H\"aring-Oldenburg, are a generalisation of the BMW algebras associated with the cyclotomic Hecke algebras of type G(k,1,n) (aka Ariki-Koike algebras) and type B…
This note gives a general construction of an integrable lattice model (and a solution of the Yang-Baxter equation with spectral parameter) from a four-dimensional field theory which is a mixture of topological and holomorphic. Spin-chain…
We build the trigonometric solutions of the Yang-Baxter equation that can not be obtained from quantum groups in any direct way. The solution is obtained using the construction suggested recently from the rational conformal field theory…
We construct a universal Vertex-IRF transformation between Vertex type universal solution and Face type universal solution of the quantum dynamical Yang-Baxter equation. This universal Vertex-IRF transformation satisfies the generalized…
We develop an algebraic approach to solvable lattice models based on a chain of algebras obeyed by the models. In each subalgebra we use a unit, giving a chain of ideals. Thus, we divide the models into distinct sectors which do not mix.…
We have found a family of solvable nineteen vertex model with statistical configurations invariant by the time reversal symmetry within a systematic study of the respective Yang-Baxter relation. The Boltzmann weights sit on a degree seven…
We classify the Markov traces factoring through the Birman-Wenzl-Murakami (BMW) algebras. For this purpose, we define a common `cover' for the two variations of the BMW-algebra originating from the quantum orthogonal/symplectic duality,…
In this paper we present a new solution of the star-triangle relation having positive Boltzmann weights. The solution defines an exactly solvable two-dimensional Ising-type (edge interaction) model of statistical mechanics where the local…
Non-polynomial Baxterized solutions of reflection equations associated with affine Hecke and affine Birman-Murakami-Wenzl algebras are found. Relations to integrable spin chain models with nontrivial boundary conditions are discussed.
Some features of integrable lattice models are reviewed for the case of the six-vertex model. By the Bethe ansatz method we derive the free energy of the six-vertex model. Then, from the expression of the free energy we show analytically…
A ``dilute'' generalisation of the Birman--Wenzl--Murakami algebra is considered. It can be ``Baxterised'' to a solution of the Yang--Baxter algebra. The $D^{(2)}_{n+1}$ vertex models are examples of corresponding solvable lattice models…
The definition of a dilute braid-monoid algebra is briefly reviewed. The construction of solvable vertex and interaction-round-a-face models built on representations of the dilute Temperley-Lieb and Birman-Wenzl-Murakami algebras is…
In this note we study `a la Baxter [1] the possible integrable manifolds of the asymmetric eight-vertex model. As expected they occur when the Boltzmann weights are either symmetric or satisfy the free-fermion condition but our analysis…
We present a procedure in which known solutions to reflection equations for interaction-round-a-face lattice models are used to construct new solutions. The procedure is particularly well-suited to models which have a known fusion hierarchy…
----- Please see the pdf file for the actual abstract and important remarks, which could not be put here due to the arXiv length restrictions. ----- This thesis presents a study of the cyclotomic BMW (Birman-Murakami-Wenzl) algebras,…