Pollicott-Ruelle Resonances on Flag Manifolds

We study the resonance spectrum of the multiflow induced on a flag manifold by the action, through multiplication by the exponential map, of the Cartan subalgebra of the underlying Lie group. We give a definition of joint resonance for the flow, then prove its discreteness and existence of resonant states. We conclude by explicit characterization of the spectrum in the special cases of Projective spaces and manifolds of full flags.