Folding the W Algebras
L. Frappat, E. Ragoucy, P. Sorba
Abstract
In the same way the folding of the Dynkin diagram of A2n (resp. A2n-1) produces the Bn (resp. Cn) Dynkin diagram, the symmetry algebra W of a Toda model based on Bn (resp. Cn) can be seen as resulting from the folding of a W-algebra based on A2n (resp. A2n-1). More generally, W algebras related to the B-C-D algebra 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 corresponding to the An case. Anagously, super W algebras associated to orthosymplectic superalgebras are deduced from those relative to the unitary A(m,n) series.
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