## Abstract

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.

Original language | English |
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Pages (from-to) | 1733-1754 |

Number of pages | 22 |

Journal | Journal of Geometry and Physics |

Volume | 61 |

Issue number | 9 |

DOIs | |

Publication status | Published - Sep 2011 |

Externally published | Yes |

## Keywords

- Elliptic hypergeometric series
- Elliptic R-matrix
- Intertwining operators
- Sklyanin algebra