\(W\)-algebras for generalized Toda theories (Q1189188)

The generalized Toda theories obtained by \textit{J. Balog} et al. [Phys. Lett. B 227, 214-220 (1989); Ann. Phys. 203, 76-136 (1990; Zbl 0725.58046)] by the conformal reduction of WZNW theories possess a new class of \(W\)-algebras, namely the algebras of gauge-invariant polynomials of the reduced theories. An algorithm for the construction of base- elements for the \(W\)-algebras of all such generalized Toda theories is found, and the \(W\)-algebras for the maximal \(\text{SL}(N,\mathbb{R})\) generalized Toda theories are constructed explicitly, the primary field basis being identified.