Every reduced totally elliptic surface group representation into PSL(2,R) is either orthogonal or Deroin-Tholozan; for PSL(2,C), irreducible ones are unitary or Deroin-Tholozan, with reducible genus-zero exceptions.
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Totally elliptic surface group representations
Every reduced totally elliptic surface group representation into PSL(2,R) is either orthogonal or Deroin-Tholozan; for PSL(2,C), irreducible ones are unitary or Deroin-Tholozan, with reducible genus-zero exceptions.