Decomposition of perverse sheaves on plane line arrangements

On the complement X = C-2 - U-i=1(n) L-i to a central plane line arrangement U-i=1(n) L-i subset of C-2, a locally constant sheaf of complex vector spaces L-a is associated to any multi-index aC(n). Using the description of MacPherson and Vilonen of the category of perverse sheaves [7, 8], we obtain a criterion for the irreducibility and number of decomposition factors of the direct image j : x -> C-2 as a perverse sheaf, where j:XC2 is the canonical inclusion.