Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1991-11-22
Int. J. Mod. Phys. A7 (1992) 6053-6080
Physics
High Energy Physics
High Energy Physics - Theory
28 pages
Scientific paper
We analyze the W_N^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 W_4^3 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 non-principal embedding of sl(2) into sl(4), or equivalently, the u(2) quasi-superconformal algebra. The general aspects of the W_N^l algebras are also presented.
Depireux Didier A.
Mathieu Pierre
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