  A space of local martingales of SLE type growth processes forms a
representation of Virasoro algebra, but apart from a few simplest cases not
much is known about this representation. The purpose of this article is to
exhibit examples of representations where L_0 is not diagonalizable - a
phenomenon characteristic of logarithmic conformal field theory. Furthermore,
we observe that the local martingales bear a close relation with the fusion
product of the boundary changing fields.
  Our examples reproduce first of all many familiar logarithmic representations
at certain rational values of the central charge. In particular we discuss the
case of SLE(kappa=6) describing the exploration path in critical percolation,
and its relation with the question of operator content of the appropriate
conformal field theory of zero central charge. In this case one encounters
logarithms in a probabilistically transparent way, through conditioning on a
crossing event. But we also observe that some quite natural SLE variants
exhibit logarithmic behavior at all values of kappa, thus at all central
charges and not only at specific rational values.
