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

Hitoshi Konno

doi:10.1007/s00023-006-0292-6

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

Quantum Algebra 2009-11-11 v1 Mathematical Physics math.MP

Authors: Hitoshi Konno

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

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.

Keywords

baxter elliptic r-matrix fusion vertex-face correspondence crossing symmetry 21-vertex model intertwining vectors

Cite

@article{arxiv.math/0503726,
  title  = {Fusion of Baxter's Elliptic $R$-matrix and the Vertex-Face Correspondence},
  author = {Hitoshi Konno},
  journal= {arXiv preprint arXiv:math/0503726},
  year   = {2009}
}

Comments

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

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

Abstract

Keywords

Cite

Comments

Related papers