Intertwining operators for Sklyanin algebra and elliptic hypergeometric series

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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 languageEnglish
Pages (from-to)1733-1754
Number of pages22
JournalJournal of Geometry and Physics
Volume61
Issue number9
DOIs
Publication statusPublished - Sep 2011
Externally publishedYes

Keywords

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

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