FOLDING THE W-ALGEBRAS

In the same way the folding of the Dynkin diagram of A2n (respectively A2n+1) produces the B(n) (respectively C(n)) Dynkin diagram, the symm etry algebra W of a Toda model based on B(n) (respectively C(n)) can b e seen as resulting from the folding of a W-algebra based on A2n (resp ectively A2n-1). More generally, W algebras related to the B-C-D algeb ra series can appear from W algebras related to the unitary ones. Such an approach is in particular well adapted to obtain fusion rules of W algebras based on non simply laced algebras from fusion rules corresp onding to the A(n) case. Analogously, super W algebras associated to o rthosymplectic superalgebras are deduced from those relative to the un itary A(m, n) series.