Of course, some complexity results may collapse for unary languages but I wonder if there is somewhere a survey summarizing the known results in this case: a kind of complexity zoo for unary languages. Would you know of such a reference ?
There is no Zoo-style reference yet, but a recent automata-theoretic survey of Giovanni Pighizzini has been useful to me, especially the slides from his talk.
- Giovanni Pighizzini, Investigations on Automata and Languages over a Unary Alphabet, CIAA 2014. doi:10.1007/978-3-319-08846-4_3
One interesting question about complexity classes over a unary alphabet that is not in the above references is the strength of Valiant's class #P1, the class of counting problems over a unary alphabet (see http://epubs.siam.org/doi/abs/10.1137/0208032). Not much is known about its power, though it has natural complete problems and, like unary languages, has polynomial-size circuits.