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Goresky–MacPherson Calculus for the Affine Flag Varieties

  • Zhiwei Yun (a1)
Abstract

We use the fixed point arrangement technique developed by Goresky and MacPherson to calculate the part of the equivariant cohomology of the affine flag variety ℱ ℓ G generated by degree 2. We use this result to show that the vertices of the moment map image of ℱ ℓ G lie on a paraboloid.

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References
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[1] Atiyah, M. F. and Pressley, A. N., Convexity and Loop Groups. Arithmetic and Geometry. Progr. Math. 36, Birkhäuser Boston, Bostohn, MA, 1983, pp. 3364.
[2] Goresky, M. and Mac Pherson, R., On the spectrum of the equivariant cohomology ring. Canad. J. Math. 62(2010), 262–283 (this issue). doi:10.4153/CJ M-2010-016-4
[3] Goresky, M., Kottwitz, R., and Mac Pherson, R., Equivariant cohomology, Koszul duality and the localization theorem. Invent. Math. 131(1998), no. 1, 25–83. doi:10.1007/s002220050197
[4] Goresky, M., Homology of affine Springer fibers in the unramified case. Duke Math. J. 121(2004), no. 3, 509–561. doi:10.1215/S0012-7094-04-12135-9
[5] Kac, V., Infinite-dimensional Lie algebras. Third edition. Cambridge University Press, Cambridge, 1990.
[6] Kostant, B. and Kumar, S., The nil Hecke ring and cohomology of G/P for a Kac-Moody group G. Adv. in Math. 62(1986), no. 3, 187–237. doi:10.1016/0001-8708(86)90101-5
[7] Laszlo, Y. and Sorger, C., The line bundles on the moduli of parabolic G-bundles over curves and their sections. Ann. Sci. École Norm. Sup. 30(1997), no. 4, 499–525.
[8] Yun, Z., Goresky-Mac Pherson calculus for the affine flag varieties. ar Xiv:0712.4395.
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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