  In this note, we give an explicit counterexample to the simple loop
conjecture for representations of surface groups into PSL(2,R). Specifically,
we show that for any surface with negative Euler characteristic and genus at
least 1, there are uncountably many non-conjugate, non-injective homomorphisms
of its fundamental group into PSL(2,R) that kill no simple closed curve (nor
any power of a simple closed curve). This result is not new -- work of Louder
and Calegari for representations of surface groups into SL(2, C) applies to the
PSL(2,R) case, but our approach here is explicit and elementary.
