  If X is the complement of a hypersurface in P^n, then Kohno showed that the
nilpotent completion of the fundamental group is isomorphic to the nilpotent
completion of the holonomy Lie algebra of X. When X is the complement of a
hyperplane arrangement A, the ranks phi_k of the lower central series quotients
of the fundamental group of X are known for isolated examples, and for two
special classes: if X is hypersolvable (in which case the quadratic closure of
the cohomology ring is Koszul), or if the holonomy Lie algebra decomposes in
degree three as a direct product of local components. In this paper, we use the
holonomy Lie algebra to obtain a formula for phi_k when A is a subarrangement
of A_n. This extends Kohno's result for braid arrangements, and provides an
instance of an LCS formula for arrangements which are not decomposable or
hypersolvable.
