Poisson harmonic forms, Kostant harmonic forms, and the $S^1$-equivariant cohomology of $K/T$
| dc.creator | Evens, Sam | |
| dc.creator | Lu, Jiang-Hua | |
| dc.date | 1997-11-26 | |
| dc.date.accessioned | 2026-07-07T03:24:37Z | |
| dc.date.available | 2026-07-07T03:24:37Z | |
| dc.description | We characterize the harmonic 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 harmonic 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 $ρ$. Using a simple argument in equivariant cohomology, we recover the connection between the Kostant harmonic forms and the Schubert calculus on $K/T$ that was found by Kostant and Kumar in 1986. We also show that the Kostant harmonic forms are limits of the more familiar Hodge harmonic forms with respect to a family of Hermitian metrics. | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9711019 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9711019 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/33395 | |
| dc.subject | Differential Geometry | |
| dc.subject | Quantum Algebra | |
| dc.title | Poisson harmonic forms, Kostant harmonic forms, and the $S^1$-equivariant cohomology of $K/T$ | |
| dc.type | text |