Abstract: The BGG complexes were originally defined in the language of homomorphisms of (generalized) Verma modules. Infinitesimal characters of the modules involved in the complex were always regular. A geometric version of them is formulated using intertwining differential operators acting among induced representations. The BGG sequences on manifolds with a given parabolic structure were constructed later as a 'curved' version of this geometric BGG complexes.

The aim of aim lecture is to describe some geometric constructions of analogues of the BGG complexes for the case of singular infinitesimal character for certain flat (resp. curved) parabolic geometries.