Intersection cohomology of Drinfeld's compactifications

TL;DR

This paper provides an explicit description of the intersection cohomology sheaf of Drinfeld's compactification of P-bundles on a smooth curve, using combinatorics of the Langlands dual Lie algebra.

Contribution

It offers a novel explicit combinatorial description of the intersection cohomology sheaf for Drinfeld's compactification, connecting geometric and Lie algebraic structures.

Findings

Explicit formula for intersection cohomology sheaf

Connection between geometry of compactification and Langlands dual algebra

Enhanced understanding of moduli stacks of P-bundles

Abstract

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 $\check{\mathfrak g}$.