Poisson harmonic forms, Kostant harmonic forms, and the $S^1$-equivariant cohomology of $K/T$

Sam Evens, Jiang-Hua Lu

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-…