  Multipolar interactions are derived in the orbitally degenerate Anderson
lattice with a spherical Fermi surface and one conduction electron per unit
cell of the simple cubic lattice. As the crystalline-electric-field (CEF)
ground state of $f^1$ configuration, the four-fold degenerate $\Gamma_8$ is
mainly studied. Intersite interactions up to a sufficiently distant pair are
Fourier transformed to the wavenumber space. For the $\Gamma_8$ case,
quadrupolar and octupolar interactions favor the staggered order with $\mib{q}
= (1/2,1/2,1/2)$, while the dipolar interaction favors an incommensurate
magnetic structure with a long modulation period. The latter is due to a Kohn
anomaly which is found to be sharply peaked for interaction channels with large
angular momenta. Implications of results are discussed for multipole orders in
CeB$_6$, and the incommensurate magnetic structure in a quasi-cubic system
CeB$_2$C$_2$.
