Propagation theorem for sheaves and applications to microdifferential systems (Q1091652)

This paper is deeply related to the theory of ``microlocal study of sheaves'' due to \textit{M. Kashiwara} and \textit{P. Schapira} [Astérisque 128 (1985; Zbl 0589.32019)]. They constructed the bifunctor \(\mu\) Hom(, ), which is a generalization of the functor of Sato's microlocalization. This paper deals with a propagation theorem for \(\mu\) Hom(F,G) if the microsupports of F and G are included in an involutory submanifold of the cotangent bundle of the base space. Important is the fact that we can recover many theorems concerning propagation of singularities for hyperbolic microdifferential systems with involutory characteristics. For example, we can regain the fundamental result for hyperbolic systems with constant multiplicities due to \textit{M. Sato, T. Kawai} and \textit{M. Kashiwara} [Lect. Notes Math. 287, 263-529 (1973; Zbl 0277.46039)]. We also recover the theorem of propagation of 2nd microlocal singularities for systems with conical involutory refraction [see J. Math. Pures Appl. 67, 1-15 (1988; Zbl 0615.58038); Ann. Inst. Fourier 37, 239-260 (1987; Zbl 0607.58041)]. Moreover we give additional results concerning 2nd microlocal analysis.