  It has recently been shown that the maximal kinematical invariance group of
polytropic fluids, for smooth subsonic flows, is the semidirect product of
SL(2,R) and the static Galilei group G. This result purports to offer a
theoretical explanation for an intriguing similarity, that was recently
observed, between a supernova explosion and a plasma implosion. In this paper
we extend this result to discuss the symmetries of discontinuous flows, which
further validates the explanation by taking into account shock waves, which are
the driving force behind both the explosion and implosion. This is accomplished
by constructing a new set of Rankine-Hugoniot conditions, which follow from
Noether's conservation laws. The new set is dual to the standard
Rankine-Hugoniot conditions and is related to them through the SL(2,R)
transformations. The entropy condition, that the shock needs to satisfy for
physical reasons, is also seen to remain invariant under the transformations.
