  A microscopic model for analyzing the microwave absorption properties of a
pinned, two-dimensional Wigner crystal in a strong perpendicular magnetic field
is developed. The method focuses on excitations within the lowest Landau level,
and corresponds to a quantum version of the harmonic approximation. For pure
systems (no disorder), the method reproduces known results for the collective
mode density of states of this system, and clearly identifies the origin of
previously unexplained structure in this quantity. The application of the
method to a simple diagonal disorder model uncovers a surprising result: a
sharp (delta-function) response at zero temperature that is consistent with
recent experiments. A simple spin lattice model is developed that reproduces
the results of the quantum harmonic approximation, and shows that the sharp
response is possible because the size scale $L_c$ of patches moving together in
the lowest frequency collective mode is extremely large compared to the sample
size for physically relevant parameters. This result is found to be a direct
repercussion of the long-range nature of the Coulomb interaction. Finally, the
model is used to analyze different disorder potentials that may pin the Wigner
crystal, and it is argued that interface disorder is likely to represent the
dominant pinning source for the system. A simple model of the interface is
shown to reproduce some of the experimental trends for the magnetic field
dependence of the pinning resonance.
