Uhlenbeck Spaces for double-struck A sign2 and Affine Lie Algebra sln

Michael Finkelberg, Dennis Gaitsgory, Alexander Kuznetsov

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

We introduce an Uhlenbeck closure of the space of based maps from projective line to the Kashiwara flag scheme of an untwisted affine Lie algebra. For the algebra sln this space of based maps is isomorphic to the moduli space of locally free parabolic sheaves on P1 × P 1 trivialized at infinity. The Uhlenbeck closure admits a resolution of singularities: the moduli space of torsion free parabolic sheaves on P 1 × P1 trivialized at infinity. We compute the Intersection Cohomology sheaf of the Uhlenbeck space using this resolution of singularities. The moduli spaces of parabolic sheaves of various degrees are connected by certain Hecke correspondences. We prove that these correspondences define an action of sln in the cohomology of the above moduli spaces.

Original languageEnglish
Pages (from-to)721-766
Number of pages46
JournalPublications of the Research Institute for Mathematical Sciences
Volume39
Issue number4
DOIs
Publication statusPublished - Dec 2003
Externally publishedYes

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