Spin orbit effects in a GaAs quantum dot in a parallel magnetic field

We analyze the effects of spin-orbit coupling on fluctuations of the conductance of a quantum dot fabricated in a GaAs heterostructure. We argue that spin-orbit effects may become important in the presence of a large parallel magnetic field B_{||}, even if they are negligble for B_{||}=0. This should be manifest in the level repulsion of a closed dot, and in reduced conductance fluctuations in dots with a small number of open channels in each lead, for large B_{||}. Our picture is consistent with the experimental observations of Folk et al.