  Martingales often play an important role in computations with Schramm-Loewner
evolutions (SLEs). The purpose of this article is to provide a straightforward
approach to the Virasoro module structure of the space of local martingales for
variants of SLEs. In the case of ordinary chordal SLE, it has been shown in
Bauer & Bernard: Phys.Lett.B 557 that polynomial local martingales form a
Virasoro module. We will show for more general variants that the module of
local martingales has a natural submodule M that has the same interpretation as
the module of polynomial local martingales of chordal SLE, but it is in many
cases easy to find more local martingales than that. We discuss the
surprisingly rich structure of the Virasoro module M and construction of the
``SLE state'' or ``martingale generating function'' by Coulomb gas formalism.
In addition, Coulomb gas or Feigin-Fuchs integrals will be shown to
transparently produce candidates for multiple SLE pure geometries.
