  Let X be the third exterior power of a six-dimensional complex vector space,
equipped with the natural action of the group GL_6(C) of invertible linear
transformations of C^6. We describe explicitly the category of
GL_6(C)-equivariant coherent D_X-modules as the category of representations of
a quiver with relations, which has finite representation type. We give a
construction of the six simple equivariant D_X-modules and give formulas for
the characters of their underlying GL_6(C)-structures. We describe the
(iterated) local cohomology groups with supports given by orbit closures,
determining, in particular, the Lyubeznik numbers associated to the orbit
closures.
