Folding the W Algebras

Abstract

In the same way the folding of the Dynkin diagram of A_{2n} (resp. A_{2n-1}) produces the B_n (resp. C_n) Dynkin diagram, the symmetry algebra W of a Toda model based on B_n (resp. C_n) can be seen as resulting from the folding of a W-algebra based on A_{2n} (resp. A_{2n-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 A_n case. Anagously, super W algebras associated to orthosymplectic superalgebras are deduced from those relative to the unitary A(m,n) series.

27 pages, Latex

References in corpus (2)

• W-symmetry in Conformal Field Theory
• On the General Structure of Hamiltonian Reductions of the Wznw Theory

Cited by in corpus (12)

• Coset Realization of Unifying W-Algebras
• A Class of W-Algebras with Infinitely Generated Classical Limit
• Classification of Structure Constants for W-algebras from Highest Weights
• Twisted Yangians and folded W-algebras
• Geometry of Higgs and Toda Fields on Riemann Surfaces
• W-superalgebras as truncation of super-Yangians
• The OPEs of Spin-4 Casimir Currents in the Holographic SO(N) Coset Minimal Models
• Classical W-algebras in types A, B, C, D and G
• More on Affine Dynkin Quiver Yangians
• Generators of Supersymmetric Classical $W$-algebras
• Gauged W Algebras
• Characteristic Dynkin diagrams and W-algebras