The Vertex-Face Correspondence and the Elliptic 6j-symbols

Details The Vertex-Face Correspondence and the Elliptic 6j-symbols The Vertex-Face Correspondence and the Elliptic 6j-symbols

2005-03-31

arxiv.org/abs/math/0503725v1

Mathematics

Quantum Algebra

23 pages

Scientific paper

10.1007/s11005-005-7647-7

A new formula connecting the elliptic $6j$-symbols and the fusion of the vertex-face intertwining vectors is given. This is based on the identification of the $k$ fusion intertwining vectors with the change of base matrix elements from Sklyanin's standard base to Rosengren's natural base in the space of even theta functions of order $2k$. The new formula allows us to derive various properties of the elliptic $6j$-symbols, such as the addition formula, the biorthogonality property, the fusion formula and the Yang-Baxter relation. We also discuss a connection with the Sklyanin algebra based on the factorised formula for the $L$-operator.

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