Residue formulas for push-forwards in equivariant cohomology: a symplectic approach

In [7] Guillemin and Kalkman proved how the nonabelian localization theorem of Jeffrey and Kirwan ([10]) can be rephrased in terms of certain iterated residue maps, in the case of torus actions. In [19] we describe the push-forward in equivariant cohomology of homogeneous spaces of classical Lie groups, with the action of the maximal torus, in terms of iterated residues at infinity of certain complex variable functions. The aim of this paper is to show how, in the special case of classical Grassmannians, the residue formulas obtained in [19] can be deduced from the ones described in [10] and [7].

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The author was partially supported by NCN grant 2015/17/N/ST1/02327.

Received 29 September 2015

Accepted 7 February 2018

Published 26 February 2019