Propagation of the Irregularity of a Microdifferential System

Abstract

We construct the functor of microlocal analytic irregularity _Iμ_hom(∙, OX) which gives a natural third term of a distinguished triangle associated to the transformation _tμ_hom(∙, OX) → _μ_hom(∙, OX) of functors on the derived category of ℝ-constructible sheaves. When restricting to ℂ-constructible objects we prove that the microlocal irregularity of a microdifferential system propagates along non 1-microcharacteristic directions, as a consequence of the propagation for _tμ_hom(∙, OX) and _μ_hom(∙, OX).