We show that there is (p-1)(p'-1) dimensional semi-relative BRST cohomology
at each non-positive ghost number in the (p,p') minimal conformal field theory
coupled to two dimensional quantum gravity. These closed string states are
related to currents and symmetry charges of `exotic' ghost number. We
investigate the symmetry structure generated by the most conventional currents
(those of vanishing total ghost number), and make a conjecture about the
extended algebra which results from incorporating the currents at negative
ghost number.Comment: 15 page