  Suppose that k is a field of characteristic zero, X is an r by s matrix of
indeterminates, where r \leq s, and R = k[X] is the polynomial ring over k in
the entries of X. We study the local cohomology modules H^i_I(R), where I is
the ideal of R generated by the maximal minors of X. We identify the indices i
for which these modules vanish, compute H^i_I(R) at the highest nonvanishing
index, i = r(s-r)+1, and characterize all nonzero ones as submodules of certain
indecomposable injective modules. These results are consequences of more
general theorems regarding linearly reductive groups acting on local cohomology
modules of polynomial rings.
