  We discuss the weak-coupling BCS theory of the heavy fermion superconductor
UPt_3, accounting for that system's anisotropic, multisheeted Fermi surface by
expanding the order parameter and pair potential in terms of appropriate basis
functions of the irreducible representations of the D_6h crystal point group.
Within a phenomenological model for the electronic structure of UPt_3 chosen to
capture the qualitative features of local density functional calculations and
de Haas-van Alphen measurements, we show how Fermi surface anisotropy can favor
pairing in certain symmetry classes, and influence the phase diagram of
unconventional superconductors. We also calculate the Ginzburg-Landau
coefficients, focussing on those coefficients relevant to current theories of
the UPt_3 phase diagram.
