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} $ .