PreprintClassical \(\mathcal{W}\)algebras in types \(A\), \(B\), \(C\), \(D\) and \(G\)A. I. Molev and E. RagoucyAbstractWe produce explicit generators of the classical \(\mathcal{W}\)algebras associated with the principal nilpotents in the simple Lie algebras of all classical types and in the exceptional Lie algebra of type \(G_2\). The generators are given by determinant formulas in the context of the Poisson vertex algebras. We also show that the images of the Walgebra generators under the Chevalleytype isomorphism coincide with the elements defined via the corresponding Miura transformations. This paper is available as a pdf (288kB) file.
