Intertwining operators for Sklyanin algebra and elliptic hypergeometric series

Details Intertwining operators for Sklyanin algebra and elliptic hypergeometric series Intertwining operators for Sklyanin algebra and elliptic hypergeometric series

2010-12-06

arxiv.org/abs/1012.1228v2

J.Geom.Phys.61:1733-1754,2011

Physics

Mathematical Physics

33 pages, 11 figures, minor changes, references added

Scientific paper

10.1016/j.geomphys.2011.02.019

Intertwining operators for infinite-dimensional representations of the Sklyanin algebra with spins l and -l-1 are constructed using the technique of intertwining vectors for elliptic L-operator. They are expressed in terms of elliptic hypergeometric series with operator argument. The intertwining operators obtained (W-operators) serve as building blocks for the elliptic R-matrix which intertwines tensor product of two L-operators taken in infinite-dimensional representations of the Sklyanin algebra with arbitrary spin. The Yang-Baxter equation for this R-matrix follows from simpler equations of the star-triangle type for the W-operators. A natural graphic representation of the objects and equations involved in the construction is used.

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