Abstract
We analyze the WN(l) algebras according to their conjectured realization as the second Hamiltonian structure of the integrable hierarchy resulting from the interchange of x and t in the l th flow of the sl (N) KdV hierarchy. The W4(3) algebra is derived explicitly along these lines, thus providing further support for the conjecture. This algebra is found to be equivalent to that obtained by the method of Hamiltonian reduction. Furthermore, its twisted version reproduces the algebra associated to a certain nonprincipal embedding of sl(2) into sl(4), or equivalently, the u(2) quasi-superconformal algebra. General aspects of the WN(l) algebras are also presented. We point out in particular that the x↔t interchange approach of the WN(l) algebra appears straightforward only when N and l are coprime.
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