Fock模中量子环形代数$U_{q,t}(\overset{..}{gl}_1)$的$R$ -矩阵
The $R$-matrix of the quantum toroidal algebra $U_{q,t}(\overset{..}{gl}_1)$ in the Fock module
摘要：
提出了一种由Hopf代数中的余积关系计算Fock模张量积上的$R$ -矩阵$R$的方法.我们将这种方法应用到量子环形代数$U_{q,t}(\overset{..}{gl}_1)$，其中$R$目前还不明确。我们证明了$U_{q,t}(\overset{..}{gl}_1)$的余积关系简化为$R$的一个简单的方程。利用对称Macdonald多项式的理论，我们表明，这个方程提供了一个递归公式的矩阵元素的$R$。
英文摘要：
We propose a method to compute the $R$-matrix $R$ on a tensor product of Fock modules from coproduct relations in a Hopf algebra. We apply this method to the quantum toroidal algebra $U_{q,t}(\overset{..}{gl}_1)$ for which $R$ is currently not explicitly known. We show that the coproduct relations of $U_{q,t}(\overset{..}{gl}_1)$ reduce to a single elegant equation for $R$. Using the theory of symmetric Macdonald polynomials we show that this equation provides a recursive formula for the matrix elements of $R$.
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