  Let $X$ be a smooth complete curve, $G$ be a reductive group and $P\subset G$
a parabolic.
  Following Drinfeld, one defines a compactification $\widetilde{\on{Bun}}_P$
of the moduli stack of $P$-bundles on $X$.
  The present paper is concerned with the explicit description of the
Intersection Cohomology sheaf of $\widetilde{\on{Bun}}_P$. The description is
given in terms of the combinatorics of the Langlands dual Lie algebra
$\check{\mathfrak g}$.
