Are there specific conditions that allow humans to see ultraviolet wavelengths
You will be interested in Aphakia, which is the lack of an eye lens usually through surgery but sometimes from birth.  These individuals supposedly see UV as a whitish-blue or whitish-violet:


  This appears to be because the three types of colour receptor (red, green and blue) have similar sensitivity to ultraviolet, so it comes out as a mixture of all three - basically white, but slightly blue because the blue sensors are somewhat better at picking up UV.1