Intertwining operators for Sklyanin algebra and elliptic hypergeometric series |
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Authors: | A. Zabrodin |
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Affiliation: | Institute of Biochemical Physics, 4 Kosygina st., 119334, Moscow, Russia; ITEP, 25 B.Cheremushkinskaya, 117218, Moscow, Russia |
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Abstract: | Intertwining operators for infinite-dimensional representations of the Sklyanin algebra with spins ? and −?−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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Keywords: | Sklyanin algebra Elliptic R-matrix Elliptic hypergeometric series Intertwining operators |
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