论文标题
Fock Module中的Quantum toroidal代数的$ r $ -Matrix
The $R$-matrix of the quantum toroidal algebra $U_{q,t}(\overset{..}{gl}_1)$ in the Fock module
论文作者
论文摘要
我们提出了一种方法，以计算Hopf代数中相关关系的Fock模块的张量产品中的$ r $ -matrix $ r $。我们将此方法应用于量子环形代数$ u_ {q，t}（\ overset {..} {gl} _1）$当前尚不明确知道的$ r $。我们表明，$ u_ {q，t}（\ Overset {..} {Gl} _1）$的共同关系关系将$降低到$ r $的单个优雅方程。使用对称麦克唐纳多项式的理论，我们表明该方程为$ r $的矩阵元素提供了递归公式。
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 $R$.
