Sklyanin代数与椭圆超几何级数的交织算子
Intertwining operators for Sklyanin algebra and elliptic hypergeometric series
摘要：
利用椭圆L-算子的交织向量技术，构造了自旋为l和-l-1的Sklyanin代数的无限维表示的交织算子.它们表示为带算子变元的椭圆超几何级数。得到的交织算子（W-算子）作为构建块的椭圆R-矩阵交织的张量积的两个L-算子在无限维表示的Sklyanin代数与任意自旋。这个R-矩阵的杨-巴克斯特方程可以从W-算子的星-三角型的简单方程得到。一个自然的图形表示的对象和方程中涉及的建设。
英文摘要：
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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