  We study the spectral properties of a system of electrons interacting through
long-range Coulomb potential on a one-dimensional chain. When the interactions
dominate over the electronic bandwidth, the charges arrange in an ordered
configuration that minimizes the electrostatic energy, forming Hubbard's
generalized Wigner lattice. In such strong coupling limit, the low energy
excitations are quantum domain-walls that behave as fractionalized charges, and
can be bound in excitonic pairs. Neglecting higher order excitations, the
system properties are well described by an effective Hamiltonian in the
subspace with one pair of domain-walls, which can be solved exactly. The
optical conducitivity $\sigma(\omega)$ and the spectral function $A(k,\omega)$
can be calculated analytically, and reveal unique features of the unscreened
Coulomb interactions that can be directly observed in experiments.
