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- W3083540206 abstract "We characterize the forms on a flag manifold $K/T$ defined by Kostant in 1963 in terms of a Poisson structure. Namely, they are ``Poisson harmonic with respect to the so-called Bruhat Poisson structure on $K/T$. This enables us to give Poisson geometrical proofs of many of the special properties of these forms. In particular, we construct explicit representatives for the Schubert basis of the $S^1$-equivariant cohomology of $K/T$, where the $S^1$-action is defined by $rho$. Using a simple argument in equivariant cohomology, we recover the connection between the Kostant forms and the Schubert calculus on $K/T$ that was found by Kostant and Kumar in 1986. We also show that the Kostant forms are limits of the more familiar Hodge forms with respect to a family of Hermitian metrics." @default.
- W3083540206 created "2020-09-11" @default.
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- W3083540206 date "1997-11-01" @default.
- W3083540206 modified "2023-09-26" @default.
- W3083540206 title "Poisson harmonic forms, Kostant harmonic forms, and the $S^1$-equivariant cohomology of $K/T$" @default.
- W3083540206 hasPublicationYear "1997" @default.
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