  Two chiral aspects of the SL(2,R) WZW model in an operator formalism are
investigated. First, the meaning of duality, or conjugation, of primary fields
is clarified. On a class of modules obtained from the discrete series it is
shown, by looking at spaces of two-point conformal blocks, that a natural
definition of contragredient module provides a suitable notion of conjugation
of primary fields, consistent with known two-point functions. We find strong
indications that an apparent contradiction with the Clebsch-Gordan series of
SL(2,R), and proposed fusion rules, is explained by nonsemisimplicity of a
certain category. Second, results indicating an infinite cyclic simple current
group, corresponding to spectral flow automorphisms, are presented. In
particular, the subgroup corresponding to even spectral flow provides part of a
hypothetical extended chiral algebra resulting in proposed modular invariant
bulk spectra.
