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Infinitely many commuting operators for the elliptic quantum group $U_{q,p}(\hat{sl_N})$ (1101.4084v1)

Published 21 Jan 2011 in nlin.SI, math-ph, and math.MP

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

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