Infinitely many commuting operators for the elliptic quantum group $U_{q,p}(\widehat{s{l}_N})$

We construct two classes of infinitely many commuting operators associated with the elliptic quantum group $U_{q,p}(\widehat{s{l}_N})$. We call one of them the integral of motion ${\mathcal{G}}_m$, $(m\in \mathbb{N})$ and the other the boundary transfer matrix $T_B(z)$, $(z\in \mathbb{C})$. The integral of motion ${\mathcal{G}}_m$ is related to elliptic deformation of the $N$-th KdV theory. The boundary transfer matrix $T_B(z)$ is related to the boundary $U_{q,p}(\widehat{s{l}_N})$ 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 ${\mathcal{G}}_m$ is open problem even for the simplest case $U_{q,p}(\widehat{s{l}_2})$.