Calabi quasimorphisms for monotone coadjoint orbits

Abstract

We show the existence of Calabi quasimorphisms on the universal covering of the group of Hamiltonian diffeomorphisms of a monotone coadjoint orbit of a compact Lie group. We show that this result follows from positivity results of Gromov-Witten invariants and the fact that the quantum product of Schubert classes can never be zero.

arXiv commentThe new version of this paper contains an upper bound for the Hofer-Zehnder capacity of coadjoint orbits of compact Lie groups. We showed that this upper bound is sharp for flag manifolds