Related papers: Affine Birman-Wenzl-Murakami Algebras and Tangles …
We introduce a BMW type algebra for every Coxeter group. These new algebras are introduced as deformations of the Brauer type algebras introduced by the author, they have the corresponding Hecke algebras as quotients.
We study the algebras underlying solvable lattice models of the type fusion interaction round the face (IRF). We propose that the algebras are universal, depending only on the number of blocks, which is the degree of polynomial equation…
The cyclotomic Birman-Murakami-Wenzl (or BMW) algebras B_n^k, introduced by R. Haring-Oldenburg, are extensions of the cyclotomic Hecke algebras of Ariki-Koike, in the same way as the BMW algebras are extensions of the Hecke algebras of…
We prove an integral version of the Schur--Weyl duality between the specialized Birman--Murakami--Wenzl algebra $B_n(-q^{2m+1},q)$ and the quantum algebra associated to the symplectic Lie algebra sp_{2m}. In particular, we deduce that this…
We give a presentation of the Kauffman (BMW) skein algebra of the torus, which is the "type BCD" analogue of the Homflypt skein algebra of torus which was computed by the first and third authors. In the appendix we show this presentation is…
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…
A complete system of pairwise orthogonal minimal idempotents for Birman-Murakami-Wenzl algebras is obtained by a consecutive evaluation of a rational function in several variables on sequences of quantum contents of up-down tableaux. A…
We treat here interaction round the face (IRF) solvable lattice models. We study the algebraic structures underlining such models. For the three block case, we show that the Yang Baxter equation is obeyed, if and only if, the…
Many of the known solutions of the Yang-Baxter equation, which are related to solvable lattice models of vertex- and IRF-type, yield representations of the Birman-Wenzl-Murakami algebra. From these, representations of a two-colour…
A new class of associative algebras referred to as affine walled Brauer algebras are introduced. These algebras are free with infinite rank over a commutative ring containing 1. Then level two walled Brauer algebras over C are defined,…
We establish a framework for cellularity of algebras related to the Jones basic construction. Our framework allows a uniform proof of cellularity of Brauer algebras, ordinary and cyclotomic BMW algebras, walled Brauer algebras, partition…
The Morita equivalences of classical Brauer algebras and classical Birman-Murakami-Wenzl algebras have been well studied. Here we study the Morita equivalence problems on these two kinds of algebras of simply-laced type, especially for them…
In this paper we first present a Birman-Murakami-Wenzl type algebra for every Coxeter system of rank 2 (corresponding to dihedral groups). We prove they have semisimple for generic parameters, and having natural cellular structures. And…
We introduce a generating function approach to the affine Brauer and Kauffman categories and show how it allows one to efficiently recover important sets of relations in these categories. We use this formalism to deduce restrictions on…
We consider integrable open spin chains related to the quantum affine algebras U_q(o(3)) and U_q(A_2^{(2)}). We discuss the symmetry algebras of these chains with the local C^3 space related to the Birman-Wenzl-Murakami algebra. The…
We study framizations of algebras through the idea of Schur--Weyl duality. We provide a general setting in which framizations of algebras such as the Yokonuma--Hecke algebra naturally appear and we obtain this way a Schur--Weyl duality for…
Affine W-algebras are a somewhat complicated family of (topological) associative algebras associated with a semisimple Lie algebra, quantizing functions on the algebraic loop space of Kostant's slice. They have attracted a great deal of…
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 define a family of algebras \mathsf{FH}_{m} which generalise the Farahat-Higman algebra introduced in [FH59] by replacing the role of the center of the group algebra of the symmetric groups with centraliser algebras of symmetric groups.…
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…