  We derive a universal Hamiltonian for a quantum dot in the presence of
spin-orbit interaction in the symmetry limits of a strong spin-dependent
Aharonov-Bohm-like term. We also derive a closed expression for the conductance
through such a dot, and use it to study the effects of spin-orbit on the
conductance peak statistics in the presence of an exchange interaction. For a
realistic strength of the exchange interaction, we find that the width of the
peak-spacing distribution is sensitive to spin-orbit coupling only in the
absence of an orbital magnetic field. We also find that spin-orbit coupling
modifies the shape of the peak-spacing distribution and suppresses the
peak-height fluctuations.
