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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 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 repr
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 diffe
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 auxi
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
We give a bosonization of the quantum affine superalgebra $U_q(widehat{sl}(N|1))$ for an arbitrary level $k in {bf C}$. The bosonization of level $k in {bf C}$ is completely different from those of level $k=1$. From this bosonization, we induce the W