Intersection cohomology of Drinfeld‚s compactifications

Abstract.

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