We discuss the modular invariance of the SL(2,R) WZW model. In particular, we
discuss in detail the modular invariants using the \hat{sl}(2,R) characters
based on the discrete unitary series of the SL(2,R) representations. The
explicit forms of the corresponding characters are known when no singular
vectors appear. We show, for example, that from such characters modular
invariants can be obtained only when the level k < 2 and infinitely large spins
are included. In fact, we give a modular invariant with three variables
Z(z,\tau, u) in this case. We also argue that the discrete series characters
are not sufficient to construct a modular invariant compatible with the
unitarity bound, which was proposed to resolve the ghost problem of the SL(2,R)
strings.Comment: 12 pages, no figures, latex; v2: a reference added, minor
corrections; v3: some changes in presentation, version to appear in Phys.
Lett.
