  We give a complete classification of irreducible symmetric spaces for which
there exist proper SL(2,R)-actions as isometries, using the criterion for
proper actions by T. Kobayashi [Math. Ann. '89] and combinatorial techniques of
nilpotent orbits. In particular, we classify irreducible symmetric spaces that
admit surface groups as discontinuous groups, combining this with Benoist's
theorem [Ann. Math. '96].
