Let
be an algebraically closed field of characteristic
,
a universal Chevalley group over
with an irreducible root system
,
a basis of
,
the set of radical weights that are nonnegative with respect to the natural ordering associated with
,
the set of dominant weights, and
the maximum of the squares of the ratios of the lengths of the roots in
. It is well known that
if
is of type
,
,
,
, or
,
if
is of type
,
, or
, and
if
is of type
. A rational representation
is called infinitesimally irreducible if its differential
defines an irreducible representation of the Lie algebra
of the group
. Let
be a simple complex Lie algebra with the same root system as
. In this paper it is proved that for
the system of weights of an infinitesimally irreducible representation
of a group
with highest weight
coincides with the system of weights of an irreducible complex representation
of a Lie algebra
with the same highest weight. In particular, the set of dominant weights of the representation
is
. Bibliography: 7 titles.