Mathematical Research Letters

Volume 8, Issue 3, May 2001 pp. 331-345.

Vertex-IRF transformations and quantization of dynamical $r$-matrices

Authors: Pavel Etingof and Dmitri Nikshych
Author institution: Massachusetts Institute of Technology, and UCLA

Summary: 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.

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