Abstract
Let G be an almost simple simply connected group over ℂ, and let Bun a G (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 \( \mathfrak{U}_G^a \) of Bun a G (ℙ2, ℙ1), which classifies, roughly, pairs (ℱG, D), where D is a 0-cycle on \( \mathbb{A}^2 = \mathbb{P}^2 - \mathbb{P}^1 \) of degree b, and ℱG is a point of Bun a−b G (ℙ2, ℙ1), for varying b.
In addition, we calculate the stalks of the Intersection Cohomology sheaf of \( \mathfrak{U}_G^a \). To do that we give a geometric realization of Kashiwara’s crystals for affine Kac-Moody algebras.
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Braverman, A., Finkelberg, M., Gaitsgory, D. (2006). Uhlenbeck Spaces via Affine Lie Algebras. In: Etingof, P., Retakh, V., Singer, I.M. (eds) The Unity of Mathematics. Progress in Mathematics, vol 244. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4467-9_2
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DOI: https://doi.org/10.1007/0-8176-4467-9_2
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