  Relying on work of Kashiwara-Schapira and Schmid-Vilonen, we describe the
behaviour of characteristic cycles with respect to the operation of geometric
induction, the geometric counterpart of taking parabolic or cohomological
induction in representation theory. By doing this, we are able to describe to
some extent the characteristic cycle associated to an induced representation,
in terms of the characteristic cycle of the representation being induced. More
precisely, under the hypothesis that the infinitesimal character is regular
(and dominant), we show that the characteristic cycle of an induced
representation splits in two terms. We describe the first term precisely, but
we are not able to do the same for the second one. What we are able to say, is
that this second term is supported on the boundary of the space generated by
the inclusion in the flag variety of $G$, of the flag variety of the Levi
subgroup. As a consequence, we prove that the cohomology packets defined by
Adams and Johnson are micro-packets, that is to say that the cohomological
constructions of Adams-Johnson are particular cases of the sheaf-theoretic ones
of Adams-Barbasch-Vogan.
