Baxter operators for arbitrary spin
Abstract
We construct Baxter operators for the homogeneous closed XXX spin chain with the quantum space carrying infinite or finitedimensional sℓ representations. All algebraic relations of Baxter operators and transfer matrices are deduced uniformly from YangBaxter relations of the local building blocks of these operators. This results in a systematic and very transparent approach where the cases of finite and infinitedimensional 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.
 Publication:

Nuclear Physics B
 Pub Date:
 January 2012
 DOI:
 10.1016/j.nuclphysb.2011.08.029
 arXiv:
 arXiv:1106.4991
 Bibcode:
 2012NuPhB.854..393C
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Quantum Algebra
 EPrint:
 37 pages LaTex, 7 figures, version for publication