Mathematical Research Letters
Volume 8 (2001)
Vertex-IRF transformations and quantization of dynamical $r$-matrices
Pages: 331 – 345
Motivated by the correspondence between the vertex and IRF models in statistical mechanics, we define and study a notion of vertex-IRF transformation for dynamical twists that generalizes a usual gauge transformation. We use vertex-IRF transformations to quantize all completely degenerate dynamical $r$-matrices on finite-dimensional Lie algebras.