论文标题
椭圆形的麦克唐纳德·罗伊塞纳族运算符和r-matrix身份的各向异性自旋概括
Anisotropic spin generalization of elliptic Macdonald-Ruijsenaars operators and R-matrix identities
论文作者
论文摘要
我们建议根据$ {\ rm gl} _m $的基本表示，就椭圆形的baxter-belavin $ r $ -matrix表示通勤矩阵值差的运算符。在标量案例中，$ m = 1 $这些操作员是椭圆形的麦克唐纳 - 鲁伊塞纳族运营商，而在一般情况下，它们可以被视为量子旋转ruijsenaars汉密尔顿人的各向异性版本。我们表明，对于任何$ m $，运营商的通勤性等同于一组$ r $ -matrix的身份。身份证明基于椭圆形$ r $ -MATRIX的属性，包括量子和Yang-Baxter方程。作为结果的应用，我们介绍了Q构造的Haldane-Shastry模型的椭圆概括。
We propose commuting set of matrix-valued difference operators in terms of the elliptic Baxter-Belavin $R$-matrix in the fundamental representation of ${\rm GL}_M$. In the scalar case $M=1$ these operators are the elliptic Macdonald-Ruijsenaars operators, while in the general case they can be viewed as anisotropic versions of the quantum spin Ruijsenaars Hamiltonians. We show that commutativity of the operators for any $M$ is equivalent to a set of $R$-matrix identities. The proof of identities is based on the properties of elliptic $R$-matrix including the quantum and the associative Yang-Baxter equations. As an application of our results, we introduce elliptic generalization of q-deformed Haldane-Shastry model.
