  I present a general theory of overconvergent p-adic automorphic forms and
eigenvarieties for connected reductive algebraic groups G whose real points are
compact modulo centre, extending earlier constructions due to Buzzard,
Chenevier and Yamagami for forms of GL(n). This leads to some new phenomena,
including the appearance of intermediate spaces of "semi-classical" automorphic
forms; this gives a hierarchy of interpolation spaces (eigenvarieties)
interpolating classical automorphic forms satisfying different finite slope
conditions (corresponding to a choice of parabolic subgroup of G at p). The
construction of these spaces relies on methods of locally analytic
representation theory, combined with the theory of compact operators on Banach
modules.
