  We present new exact solutions of Force-Free Electrodynamics (FFE) in the
Near-Horizon region of an Extremal Kerr black hole (NHEK) and offer a complete
classification of the subset that form highest-weight representations of the
spacetime's SL(2,R) x U(1) isometry group. For a natural choice of spacetime
embedding of this isometry group, the SL(2,R) highest-weight conditions lead to
stationary solutions with non-trivial angular dependence, as well as
axisymmetry when the U(1)-charge vanishes. In addition, we unveil a hidden
SL(2,C) symmetry of the equations of FFE that stems from the action of a
complex automorphism group, and enables us to generate an SL(2,C) family of
(generically time-dependent) solutions. We then obtain still more general
solutions with less symmetry by appealing to a principle of linear
superposition that holds for solutions with collinear currents and allows us to
resum the highest-weight primaries and their SL(2,R)-descendants.
