The Algebra of Differential Operators on the Circle and $\Wkpq$

Details The Algebra of Differential Operators on the Circle and $\Wkpq$ The Algebra of Differential Operators on the Circle and $\Wkpq$

1992-11-08

arxiv.org/abs/hep-th/9211036v2

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, Plain TeX, BONN-HE-92/34, KUL-TF-92/27, QMW-PH-92-20

Scientific paper

10.1007/BF00739580

Radul has recently introduced a map from the Lie algebra of differential operators on the circle to $\W_n$. In this note we extend this map to $\Wkpq$, a recently introduced one-parameter deformation of $\Wkp$---the second hamiltonian structure of the KP hierarchy. We use this to give a short proof that $\W_\infty$ is the symmetry algebra of additional symmetries of the KP equation. (The replaced version clears up some minor points and corrects some notational glitches. Get this one!)

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