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The Baxterization process for the dynamical Yang-Baxter equation is studied. We introduce the local dynamical Hecke ,Temperley-Lieb and Birman-Murakami-Wenzl operators, then by inserting spectral parameters, from each representation of…
The generalized Sutherland-Romer models and Yan models with internal spin degrees are formulated in terms of the Polychronakos' approach and RTT relation associated to the Yang-Baxter equation in consistent way. The Yangian symmetry is…
We introduce a new approach to the study of the crossing equation for CFTs in the presence of a boundary. We argue that there is a basis for this equation related to the generalized free field solution. The dual basis is a set of linear…
The main aim of this paper is to determine reflections to bijective and non-degenerate solutions of the Yang-Baxter equation, by exploring their connections with their derived solutions. This is motivated by a recent description of left…
Based on the tetrahedral Zamolodchikov algebra, we prove the Yang-Baxter equation for the R-matrix of 1-D SU(n) Hubbard model. Furthermore, we present a generalization of the model.
In this paper, several proposals of optically simulating Yang-Baxter equations have been presented. Motivated by the recent development of anyon theory, we apply Temperley-Lieb algebra as a bridge to recast four-dimentional Yang-Baxter…
We formulate a general set of consistency requirements, which are expected to be satisfied by the scattering matrices in the presence of reflecting boundaries. In particular we derive an equivalent to the boostrap equation involving the…
We study Zamolodchikov algebras whose commutation relations are described by Belavin matrices defining a solution of the Yang-Baxter equation (Belavin $R$-matrices). Homomorphisms of Zamolodchikov algebras into dynamical algebras with…
We introduce the notion of a matching Rota-Baxter algebra motivated by the recent work on multiple pre-Lie algebras arising from the study of algebraic renormalization of regularity structures~[10,18]. This notion is also related to…
Combining the notions of braces and relative Rota-Baxter operators on groups in connection with the Yang-Baxter equation and a factorization theorem of Lie groups from integrable systems, relative Rota-Baxter operators on braces and…
We consider involutive, non-degenerate, finite set theoretic solutions of the Yang-Baxter equation. Such solutions can be always obtained using certain algebraic structures that generalize nil potent rings called braces. Our main aim here…
We generalize the definition of Yang-Baxter basis of type $A$ Hecke algebra introduced by A.Lascoux, B.Leclerc and J.Y.Thibon (Letters in Math. Phys., 40 (1997), 75--90) to all the Lie types and prove their duality. As an application we…
We define a new class of unitary solutions to the classical Yang-Baxter equation (CYBE). These ``boundary solutions'' are those which lie in the closure of the space of unitary solutions to the modified classical Yang-Baxter equation…
Several years ago, it was proposed that the usual solutions of the Yang-Baxter equation associated to Lie groups can be deduced in a systematic way from four-dimensional gauge theory. In the present paper, we extend this picture, fill in…
We introduce a universal framework for boundary transfer matrices, inspired by Sklyanin's two-row transfer matrix approach for quantum integrable systems with boundary conditions. The main examples arise from quantum symmetric pairs of…
We generalize the classical study of (generalized) Lax pairs and the related $O$-operators and the (modified) classical Yang-Baxter equation by introducing the concepts of nonabelian generalized Lax pairs, extended $\calo$-operators and the…
Let $n \ge 2$ be a natural number, $M$ a real $n \times n$ matrix, $s$ the sum of the entries of $M$ and $q$ the sum of their squares. With $\alpha := s/n$ and $\beta := q/n$, Gasper's determinant bound says that $ |\det M| \le…
Let $ L $ be a Lie algebra over arbitrary field $ k $ with dim $ L $ =3 and dim $ L' $ =2. All solutions of constant classical Yang- Baxter equation (CYBE) in Lie algebra $ L $ are obtained and the necessary conditions which $ (L,[\…
The BH algebra is defined by two sets of generators one of which satisfy the relations of the braid group and the other the relations of the Hecke algebra of projectors.These algebras are then combined by additional relations in a way which…
By using the intertwiner and face-vertex correpondence relation, we obtain the Bethe ansatz equation of eight vertex model with open boundary condtitions in the framework of algebraic Bethe ansatz method. The open boundary condition under…