Non-Abelian bosonization and higher spin symmetries

The higher spin properties of non-Abelian bosonization in the classical theory are investigated. Both the symmetry transformation algebra and the classical current algebra for the non-Abelian free-fermionic model are linear Gel'fand-Dickey type algebras. However, for the corresponding WZNW model these algebras are different. There exist symmetry transformations whose algebra remains the linear Gel'fand-Dickey algebra, while in the corresponding current algebra, nonlinear terms arise. Moreover, this algebra is closed (in Casimir form) only in an extended current space in which nonlinear currents are included. In the affine sector, it is necessary to include higher isotopic spin current too. As a result we have a triple extended algebra.