  We prove that the local components of an automorphic representation of an
adelic semisimple group have equal rank in the sense defined earlier by the
second author. Our theorem is an analogue of the results previously obtained by
Howe, Li, Dvorsky--Sahi, and Kobayashi--Savin. Unlike previous works which are
based on explicit matrix realizations and existence of parabolic subgroups with
abelian unipotent radicals, our proof works uniformly for all of the (classical
as well as exceptional) groups under consideration. Our result is an extension
of the statement known for several semisimple groups that if at least one local
component of an automorphic representation is a minimal representation, then
all of its local components are minimal.
