Results 1 - 10 of 4437
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[en] Commutative sets of Jucys–Murphy elements for affine braid groups of types were defined. Construction of R-matrix representations of the affine braid group of type and its distinguished commutative subgroup generated by the -type Jucys–Murphy elements are given. We describe a general method to produce flat connections for the two-boundary quantum Knizhnik–Zamolodchikov equations as necessary conditions for Sklyanin's type transfer matrix associated with the two-boundary multicomponent Zamolodchikov algebra to be invariant under the action of the -type Jucys–Murphy elements. We specify our general construction to the case of the Birman–Murakami–Wenzl algebras (BMW algebras for short). As an application we suggest a baxterization of the Dunkl–Cherednik elements in the double affine Hecke algebra of type A. (paper)
[en] Orthogonal or symplectic Yangians are defined by the Yang–Baxter RLL relation involving the fundamental R matrix with or symmetry. Simple L operators with linear or quadratic dependence on the spectral parameter exist under restrictive conditions. These conditions are investigated in general form.
[en] The structure of Bethe vectors for generalized models associated with the rational and trigonometric R-matrix is investigated. The Bethe vectors in terms of two-component and multicomponent models are described. Their structure in terms of local variables and operators is provided. This, as a consequence, proves the equivalence of coordinate and algebraic Bethe ansatzes for the Heisenberg spin chains. Hermitian conjugation of the elements of the monodromy matrix for the spin chains is studied.
[en] By requiring invariance directly under the Yangian symmetry, we rederive Beisert's quantum R-matrix, in a form that carries explicit dependence on the representation labels, the braiding factors and the spectral parameters ui. In this way, we demonstrate that there exists rewriting of its entries, such that the dependence on the spectral parameters is purely of a difference form. Namely, the latter enter only in the combination u1 - u2, as indicated by the shift automorphism of the Yangian. When recasted in this fashion, the entries exhibit a cleaner structure, which allows us to spot new interesting relations among them. This permits us to package them into a practical tensorial expression, where the nondiagonal entries are taken care of by explicit combinations of symmetry algebra generators
[en] We consider the ‘universal monodromy operators’ for the Baxter Q-operators. They are given as images of the universal R-matrix in oscillator representation. We find related universal factorization formulas in the Uq( sl-hat (2)) case. (fast track communications)
[en] We consider the quantum vertex algebra associated with the trigonometric R -matrix in type A as defined by Etingof and Kazhdan. We show that its center is a commutative associative algebra and construct an algebraically independent family of topological generators of the center at the critical level. (paper)
[en] We identify the algorithm for constructing steady states of the n-species totally asymmetric simple exclusion process (TASEP) on an L site periodic chain by Ferrari and Martin with a composition of combinatorial R for the quantum affine algebra in crystal base theory. Based on this connection and the factorized form of the R matrix derived recently from the tetrahedron equation, we establish a new matrix product formula for the steady state of the TASEP, which is expressed in terms of corner transfer matrices of the q-oscillator valued five-vertex model at q = 0. (fast track communication)
[en] We describe a unifying framework for the systematic construction of integrable deformations of integrable σ-models within the Hamiltonian formalism. It applies equally to both the ‘Yang–Baxter’ type as well as ‘gauged WZW’ type deformations which were considered recently in the literature. As a byproduct, these two families of integrable deformations are shown to be Poisson–Lie T-dual of one another. (paper)
[en] The Yang—Baxter equation is reinvestigated in the framework of triple system. By requiring the rational R matrix of the Yang—Baxter equation satisfying the generalized Filippov condition, we derive a relation with respect to the rational R matrix. Moreover the case of the super Yang—Baxter equation is also investigated. (general)