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

### A. I. Molev and E. Ragoucy

#### Abstract

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