Quantum deformed magnon kinematics

The dispersion relation for planar N=4 supersymmetric Yang-Mills isidentified with the Casimir of a quantum deformed two-dimensional kinematicalsymmetry, E_q(1,1). The quantum deformed symmetry algebra is generated by themomentum, energy and boost, with deformation parameter q=e^{2\pi i/\lambda}.Representing the boost as the infinitesimal generator for translations on therapidity space leads to an elliptic uniformization with crossingtransformations implemented through translations by the elliptic half-periods.This quantum deformed algebra can be interpreted as the kinematical symmetry ofa discrete integrable model with lattice spacing given by the BMN lengtha=2\pi/\sqrt{\lambda}. The interpretation of the boost generator as the cornertransfer matrix is briefly discussed.Comment: 7 pages. Latex. v2: Misprint corrected. Added references to the previous elliptic uniformization by N. Beisert and the recent one by I. Kostov, D. Serban and D. Voli