  We prove an analogue of Kac's Theorem, describing the dimension vectors of
indecomposable coherent sheaves, or parabolic bundles, over weighted projective
lines. We use a theorem of Peng and Xiao to associate a Lie algebra to the
category of coherent sheaves for a weighted projective line over a finite
field, and find elements of this Lie algebra which satisfy the relations
defining the loop algebra of a Kac-Moody Lie algebra.
