Parabolic Hecke Eigensheaves

bundles on the projective line C with tame ramification at five points {p1, p2, p3, p4, p5}.
In particular we construct the automorphic D-modules predicted by GLC on the
moduli space of rank two parabolic bundles on (C, {p1, p2, p3, p4, p5}). The construction uses non-abelian Hodge theory and a Fourier-Mukai transform along the fibers
of the Hitchin fibration to reduce the problem to one in classical projective geometry
on the intersection of two quadrics in P4.

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