  Irreducible representations are the building blocks of general, semisimple
Galois representations \rho, and cuspidal representations are the building
blocks of automorphic forms \pi of the general linear group. It is expected
that when an object of the former type is associated to one of the latter type,
usually in terms of an identity of L-functions, the irreducibility of the
former should imply the cuspidality of the latter, and vice-versa. It is not a
simple matter - at all - to prove this expectation in either direction, and
nothing much is known in dimensions >2. The main result of this article shows
for n < 6, in particular, that the cuspidality of a regular algebraic \pi is
implied by the irreducibility of \rho.
