To clarify, is the speed limit of the universe the speed of light in a vacuum, or the speed of light in that particular medium, i.e. if the speed of light in a particular medium were only 17 m/s, would I be able to go faster than that speed?
Also, for the special relativity equations of time dilation, I was always taught to use $c$, as in the speed of light in a vacuum. But to me, it makes more sense to use $c_m$ the speed of light in that particular medium, since all the thought experiments (involving light clocks) seem to assume the speed of light in that medium is $c$, not $c_m$.
Answer
The equations of relativity do not hold in a medium, which selects a preferred coordinate system (the one which rests in the medium). Can you go faster than the local speed of the quasi-particles formed by the photons and the polarized atoms of the medium? Of course. If you are charged you will be generating Cherenkov radiation, too. See http://en.wikipedia.org/wiki/Cherenkov_radiation.
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