Lattice models, deformed Virasoro algebra and reduction equation

TL;DR

This paper investigates the fused currents of the deformed Virasoro algebra, demonstrating their behavior on cohomologies and establishing the closure of excitation systems in certain lattice models, filling a key gap in algebraic lattice model analysis.

Contribution

It constructs a homotopy operator to prove fused currents coincide on cohomologies, confirming the closure of excitation systems in specific RSOS models.

Findings

Fused currents coincide on cohomologies at special parameters.

Closeness of excitation systems in nonunitary RSOS models is proven.

Results align algebraic approach with other methods in lattice models.

Abstract

We study the fused currents of the deformed Virasoro algebra (DVA). 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 solid-on-solid (SOS) models in the transfer-matrix picture. It allows us to prove the closeness of the system of excitations for a special nonunitary series of restricted SOS (RSOS) 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.