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.

MSC Classifications:

14L30, 55N91 show english descriptions Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]
Equivariant homology and cohomology [See also 19L47] 14L30 - Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]
55N91 - Equivariant homology and cohomology [See also 19L47]

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