Classical \(\mathcal{W}\)-algebras in types \(A\), \(B\), \(C\), \(D\) and \(G\)

A. I. Molev and E. Ragoucy


We 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 W-algebra generators under the Chevalley-type isomorphism coincide with the elements defined via the corresponding Miura transformations.

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Monday, March 10, 2014