Hostname: page-component-5cf477f64f-xc2pj Total loading time: 0 Render date: 2025-04-07T16:19:49.223Z Has data issue: false hasContentIssue false
  • English
  • Français

Goresky–MacPherson Calculus for the Affine Flag Varieties

Published online by Cambridge University Press:  20 November 2018

Zhiwei Yun
Zhiwei Yun*
Affiliation:
Princeton University, Princeton, New Jersey 08544, USA, e-mail: zyun@math.princeton.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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 $\mathcal{F}{{\ell }_{G}}$ generated by degree 2. We use this result to show that the vertices of the moment map image of $\mathcal{F}{{\ell }_{G}}$ lie on a paraboloid.

Keywords

14L3055N91
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 62 , Issue 2 , 01 April 2010 , pp. 473 - 480
Copyright
Copyright © Canadian Mathematical Society 2010

References

[1] Atiyah, M. F. and Pressley, A. N., Convexity and Loop Groups. Arithmetic and Geometry. Progr. Math. 36, Birkhäuser Boston, Bostohn, MA, 1983, pp. 33–64.Google Scholar
[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-2010-016-4Google Scholar
[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/s002220050197Google Scholar
[4] Goresky, M., Homology of affine Springer fibers in the unramified case. Duke Math. J. 121(2004), no. 3, 509–561. doi:10.1215/S0012-7094-04-12135-9Google Scholar
[5] Kac, V., Infinite-dimensional Lie algebras. Third edition. Cambridge University Press, Cambridge, 1990.Google Scholar
[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)90101-5Google Scholar
[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.Google Scholar
[8] Yun, Z., Goresky-Mac Pherson calculus for the affine flag varieties. ar Xiv:0712.4395.Google Scholar