When I had my 20D converted to IR I had a chat with the guys doing it about UV photography. While the sensors used in digital cameras are sensitive to UV they normally have a UV filter in front of the sensor, so that filter would need to be removed - just like they do for the IR modification. However, there's another problem. Most normal lenses, indeed most normal glass, is exceptionally good at absorbing UV. So you'd need to use special UV-transparent glass in your lenses.
At the time (about 5 years ago) they said they were close to getting something usable using Nikon gear. But I've not heard anything since.