Open descendants extend Conformal Field Theory to unoriented surfaces with
boundaries. The construction rests on two types of generalizations of the
fusion algebra. The first is needed even in the relatively simple case of
diagonal models. It leads to a new tensor that satisfies the fusion algebra,
but whose entries are signed integers. The second is needed when dealing with
non-diagonal models, where Cardy's ansatz does not apply. It leads to a new
tensor with positive integer entries, that satisfies a set of polynomial
equations and encodes the classification of the allowed boundary operators.Comment: 19 pages, LATEX, 4 eps figures. Contribution to the Proceedings of
the CERN Meeting on STU Dualities, Dec. 9
