Infinitely many commuting operators for the elliptic quantum group $U_{q,p}(\hat{sl_N})$
Infinitely many commuting operators for the elliptic quantum group $U_{q,p}(\hat{sl_N})$
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椭圆量子群 $U_{q,p}(hat{sl_N})$ 的无穷多个交换算子
DOI：
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发表时间：
2011
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通讯作者：
T. Kojima
中科院分区：
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作者：
T. Kojima
我们构造了两类与椭圆量子群$U_{q，p}(\hat{sl_N})$有关的无穷多个交换算子。其中一个称为运动积分，$(m\in{\mathbb N})$，另一个称为边界转移矩阵$T_B(Z)$，$(z\in{\mathbb C})$。运动积分与第N阶KdV理论的椭圆形变有关。边界传递矩阵$T_B(Z)$与边界$U_{q，p}(\HAT{sl_N})$人脸模型相关。我们利用椭圆量子群的自由场实现对角化了边界转移矩阵T_B(Z)，然而运动积分的对角化是一个开放问题，即使在最简单的情况下也是如此。
We construct two classes of infinitely many commuting operators associated with the elliptic quantum group $U_{q,p}(\hat{sl_N})$. We call one of them the integral of motion ${\cal G}_m$, $(m \in {\mathbb N})$ and the other the boundary transfer matrix $T_B(z)$, $(z \in {\mathbb C})$. The integral of motion ${\cal G}_m$ is related to elliptic deformation of the $N$-th KdV theory. The boundary transfer matrix $T_B(z)$ is related to the boundary $U_{q,p}(\hat{sl_N})$ face model. We diagonalize the boundary transfer matrix $T_B(z)$ by using the free field realization of the elliptic quantum group, however diagonalization of the integral of motion ${\cal G}_m$ is open problem even for the simplest case $U_{q,p}(\hat{sl_2})$.