We construct Baxter operators for the homogeneous closed XXX spin
chain with the quantum space carrying infinite or finite dimensional sℓ2​
representations. All algebraic relations of Baxter operators and transfer
matrices are deduced uniformly from Yang-Baxter relations of the local building
blocks of these operators. This results in a systematic and very transparent
approach where the cases of finite and infinite dimensional representations are
treated in analogy. Simple relations between the Baxter operators of both cases
are obtained. We represent the quantum spaces by polynomials and build the
operators from elementary differentiation and multiplication operators. We
present compact explicit formulae for the action of Baxter operators on
polynomials.Comment: 37 pages LaTex, 7 figures, version for publicatio