Infinitely many commuting operators for the elliptic quantum group $U_{q,p}(\hat{sl_N})$
Abstract
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 $U_{q,p}(\hat{sl_2})$.
 Publication:

arXiv eprints
 Pub Date:
 January 2011
 DOI:
 10.48550/arXiv.1101.4084
 arXiv:
 arXiv:1101.4084
 Bibcode:
 2011arXiv1101.4084K
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Mathematical Physics
 EPrint:
 Proceedings for the 6th Mathematical Physics Meeting, held in Belgrade, Serbia, 2010