We just introduced , and now the idea is
to try to substituteinto our covariant ansatz (3).
It turns out that this works for some class of representations
(but not all). We will explain later what is the condition on , but for now
just proceed with the general for as long as we can.
We want to apply the ansatz of the form (3) for
. This means that we need
to find a fixed vector representing a
cohomology class of the covariant complex (6).
Since is in , we have to start with understanding
the structure of .