  It is well-known that the Pl\"ucker relations generate the ideal of relations
of the maximal minors of a generic matrix. In this paper we discuss the
relations between minors of a (non-maximal) fixed size. We will exhibit minimal
relations in degrees 2 (non-Pl\"ucker in general) and 3, and give some evidence
for our conjecture that we have found the generating system of the ideal of
relations. The approach is through the representation theory of the general
linear group.
