For noncompact semisimple Lie groups
with
finite center, we study the dynamics of the actions of their discrete subgroups
on the associated
partial flag manifolds
.
Our study is based on the observation, already made in the deep work of Benoist,
that they exhibit also in higher rank a certain form of convergence-type
dynamics. We identify geometrically domains of proper discontinuity in all
partial flag manifolds. Under certain dynamical assumptions equivalent to
the Anosov subgroup condition, we establish the cocompactness of the
–action on
various domains of proper discontinuity, in particular on domains in the full flag manifold
. In the regular case
(eg of
–Anosov
subgroups), we prove the nonemptiness of such domains if
has (locally) at least one noncompact simple factor not of the type
,
or
by
showing the nonexistence of certain ball packings of the visual boundary.
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