Mathematical Research Letters

Volume 8 (2001)

Number 3

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

Pages: 331 – 345



Pavel Etingof (Massachusetts Institute of Technology)

Dmitri Nikshych (University of California at Los Angeles)


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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