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Register a new userFactorization of R-matrix and Baxter Q-operators for generic sl(N) spin chains
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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.
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It is shown that the transfer matrices of homogeneous sl(2) invariant spin chains with generic spin, both closed and open, are factorized into the product of two operators. The latter satisfy the Baxter equation that follows from the structure of the reducible representations of the sl(2) algebra.
We study properties of transfer matrices in the sl(N) spin chain models. The transfer matrices with an infinite dimensional auxiliary space are factorized into the product of N commuting Baxter Q-operators. We consider the transfer matrices with auxiliary spaces of a special type (including the finite dimensional ones). It is shown that they can be represented as the alternating sum over the transfer matrices with infinite dimensional auxiliary spaces. We show that certain combinations of the Baxter Q-operators can be identified with the Q-functions which appear in the Nested Bethe Ansatz.
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