An algebraic formula for the Gysin homomorphism from G/B to G/P
Let G be linear, semisimple algebraic group, with Borel subgroup B, containing a maximal torus H. If P is a parabolic subgroup containing B, there is a natural projection map \(\pi\) : G/B\(\to G/P\) as well as a Gysin homomorphism (or transfer) \(\pi_*: H^*(G/B; {\mathbb{C}})\to H^*(G/P; {\mathbb{C}}).\) The principal goal of this paper is to derive an algebraic formula for \(\pi_*\). If h is the Lie algebra of H, R is the graded, symmetric algebra of \(h^*\), which admits a natural action of the Weyl group W. The authors succeed in describing \(\pi_*\) in terms of quotients of R and related algebras. The methods involve the calculation of the residues of the zeros of holomorphic vector fields and are quite technical.
residues of the zeros of holomorphic vector fields
scientific article; zbMATH DE number 4024330