Lattice models, deformed Virasoro algebra and reduction equation
Abstract
We study the fused currents of the deformed Virasoro algebra. By constructing a homotopy operator we show that for special values of the parameter of the algebra fused currents pairwise coincide on the cohomologies of the Felder resolution. Within the algebraic approach to lattice models these currents are known to describe neutral excitations of the solidonsolid (SOS) models in the transfermatrix picture. It allows us to prove the closeness of the system of excitations for a special nonunitary series of restricted SOS models. Though the results of the algebraic approach to lattice models were consistent with the results of other methods, the lack of such proof had been an essential gap in its construction.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 June 2020
 DOI:
 10.1088/17518121/ab81d6
 arXiv:
 arXiv:1911.11412
 Bibcode:
 2020JPhA...53x5202L
 Keywords:

 integrable models of statistical mechanics;
 elliptic algebras;
 free field representation;
 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Quantum Algebra
 EPrint:
 14 pages