Fusion of Baxter's Elliptic $R$-matrix and the Vertex-Face Correspondence

Details Fusion of Baxter's Elliptic $R$-matrix and the Vertex-Face Correspondence Fusion of Baxter's Elliptic $R$-matrix and the Vertex-Face Correspondence

2005-03-31

arxiv.org/abs/math/0503726v1

Mathematics

Quantum Algebra

To appear in the proceedings of the workshop ``Solvable Lattice Models 2004", July 20--23, 2004, RIMS Koukyuroku, Kyoto Univer

Scientific paper

10.1007/s00023-006-0292-6

The matrix elements of the $2\times 2$ fusion of Baxter's elliptic $R$-matrix, $R^{(2,2)}(u)$, are given explicitly. Based on a note by Jimbo, we give a formula which show that $R^{(2,2)}(u)$ is gauge equivalent to Fateev's $R$-matrix for the 21-vertex model. Then the crossing symmetry formula for $R^{(2,2)}(u)$ is derived. We also consider the fusion of the vertex-face correspondence relation and derive a crossing symmetry relation between the fusion of the intertwining vectors and their dual vectors.

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