AUTOMORPHISMS OF W-ALGEBRAS AND EXTENDED RATIONAL CONFORMAL FIELD-THEORIES

Many extended conformal algebras with one generator in addition to the Virasoro field as well as Casimir algebras have non-trivial outer aut omorphisms which enables one to impose ''twisted'' boundary conditions on the chiral fields. We study their effect on the highest-weight rep resentations. We give formulae for the enlarged rational conformal fie ld theories in both series of W-algebras with two generators and conje cture a general formula for the additional models in the minimal serie s of Casimir algebras. A third series of W-algebras with two generator s which includes the spin-three algebra at c = -2 also has finitely ma ny additional fields in the twisted sector although the model itself i s apparently not rational. The additional fields in the twisted sector have applications in statistical mechanics as we demonstrate for Z(n) -quantum spin chains with a particular type of boundary conditions.