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

Details Infinitely many commuting operators for the elliptic quantum group $U_{q,p}(\hat{sl_N})$ Infinitely many commuting operators for the elliptic quantum group $U_{q,p}(\hat{sl_N})$

2011-01-21

arxiv.org/abs/1101.4084v1

Proceedings for the 6th Mathematical Physics Meeting, held in Belgrade, Serbia, 2010

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

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 $U_{q,p}(\hat{sl_2})$.

Affiliated with

Also associated with

No associations

Rating

Infinitely many commuting operators for the elliptic quantum group $U_{q,p}(\hat{sl_N})$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Infinitely many commuting operators for the elliptic quantum group $U_{q,p}(\hat{sl_N})$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Infinitely many commuting operators for the elliptic quantum group $U_{q,p}(\hat{sl_N})$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-18776