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Register a new userBaxter Q-operators for integrable DST chain
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Following the procedure, described in the paper nlin.SI/0003002, for the integrable DST chain we construct Baxter Q-operators as the traces of monodromy of some M-operators, that act in quantum and auxiliary spaces. Within this procedure we obtain two basic M-operators and derive some functional relations between them such as intertwining relations and wronskian-type relations between two basic Q-operators.
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The noncompact homogeneous sl(3) invariant spin chains are considered. We show that the transfer matrix with generic auxiliary space is factorized into the product of three sl(3) invariant commuting operators. These operators satisfy the finite difference equations in the spectral parameters which follow from the structure of the reducible sl(3) modules.
We develop an approach for constructing the Baxter Q-operators for generic sl(N) spin chains. The key element of our approach is the possibility to represent a solution of the the Yang Baxter equation in the factorized form. We prove that such a representation holds for a generic sl(N) invariant R-operator and find the explicit expression for the factorizing operators. Taking trace of monodromy matrices constructed of the factorizing operators one defines a family of commuting (Baxter) operators on the quantum space of the model. We show that a generic transfer matrix factorizes into the product of N Baxter Q-operators and discuss an application of this representation for a derivation of functional relations for transfer matrices.
In the present paper we describe the procedure of the Q-operators construction for the q-deformed model, described by the Lax operator, which is important to formulate the Bethe ansatz for the Sin-Gordon model. This Lax operator can also be considered as some massless limit of the Lax operator of SG model. We constructed two R-operators which are the universal intertwiners for the Lax operators. The traces of its monodromies over the auxiliary space are Baxter operators i.e. the operator solutions of T-Q equation. We also found the intertwining relations which imply the mutual commutativity of the corresponding Q-operators.
The action of a Backlund-Darboux transformation on a spectral problem associated with a known integrable system can define a new discrete spectral problem. In this paper, we interpret a slightly generalized version of the binary Backlund-Darboux (or Zakharov-Shabat dressing) transformation for the nonlinear Schrodinger (NLS) hierarchy as a discrete spectral problem, wherein the two intermediate potentials appearing in the Darboux matrix are considered as a pair of new dependent variables. Then, we associate the discrete spectral problem with a suitable isospectral time-evolution equation, which forms the Lax-pair representation for a space-discrete NLS system. This formulation is valid for the most general case where the two dependent variables take values in (rectangular) matrices. In contrast to the matrix generalization of the Ablowitz-Ladik lattice, our discretization has a rational nonlinearity and admits a Hermitian conjugation reduction between the two dependent variables. Thus, a new proper space-discretization of the vector/matrix NLS equation is obtained; by changing the time part of the Lax pair, we also obtain an integrable space-discretization of the vector/matrix modified KdV (mKdV) equation. Because Backlund-Darboux transformations are permutable, we can increase the number of discrete independent variables in a multi-dimensionally consistent way. By solving the consistency condition on the two-dimensional lattice, we obtain a new Yang-Baxter map of the NLS type, which can be considered as a fully discrete analog of the principal chiral model for projection matrices.
Discrete and q-difference deformations of the structure constants for a class of associative noncommutative algebras are studied. It is shown that these deformations are governed by a central system of discrete or q-difference equations which in particular cases represent discrete and q-differenc
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