TY - CHAP

T1 - Uhlenbeck spaces via affine lie algebras

AU - Braverman, Alexander

AU - Finkelberg, Michael

AU - Gaitsgory, Dennis

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85015722943&partnerID=8YFLogxK

U2 - 10.1007/0-8176-4467-9_2

DO - 10.1007/0-8176-4467-9_2

M3 - Chapter

AN - SCOPUS:85015722943

T3 - Progress in Mathematics

SP - 17

EP - 135

BT - Progress in Mathematics

PB - Springer Basel

ER -