Uhlenbeck spaces via affine lie algebras

Alexander Braverman, Michael Finkelberg, Dennis Gaitsgory

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

56 Citations (Scopus)


Let G be an almost simple simply connected group over ℂ, and let BunG a (ℙ2, ℙ1) be the moduli scheme of principalG-bundles on the projective plane ℙ2, of second Chern class a, trivialized along a line ℙ1 ⊂ ℙ2. We define the Uhlenbeck compactification UG a of BunG a (ℙ2, ℙ1), which classifies, roughly, pairs (ℱG, D), where D is a 0-cycle on A2 = P2 - P1 of degree b, and ℱG is a point of BunG a−b (ℙ2, ℙ1), for varying b. In addition, we calculate the stalks of the Intersection Cohomology sheaf of UG a. To do that we give a geometric realization of Kashiwara’s crystals for affine Kac-Moody algebras.

Original languageEnglish
Title of host publicationProgress in Mathematics
PublisherSpringer Basel
Number of pages119
Publication statusPublished - 2006
Externally publishedYes

Publication series

NameProgress in Mathematics
ISSN (Print)0743-1643
ISSN (Electronic)2296-505X


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