Calabi quasimorphisms for monotone coadjoint orbits

TL;DR

This paper proves the existence of Calabi quasimorphisms on certain symplectic manifolds related to Lie groups, using Gromov-Witten invariants and quantum cohomology properties.

Contribution

It establishes the existence of Calabi quasimorphisms for monotone coadjoint orbits, linking symplectic topology with quantum cohomology.

Findings

Calabi quasimorphisms exist on the universal cover of Hamiltonian diffeomorphisms for these orbits.

Positivity of Gromov-Witten invariants is key to the proof.

Quantum product of Schubert classes is always non-zero in this context.

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.