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ClassicalN=1W-superalgebras from Hamiltonian reduction

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Abstract

A combinatorial proof is presented of the fact that the space of supersymmetric Lax operators admits a Poisson structure analogous to the second Gel'fand-Dickey bracket of the generalized KdV hierarchies. This allows us to prove that the space of Lax operators of odd order has a symplectic submanifold-defined by (anty)symmetric operators-which inherits a Poisson structure defining classicalW-superalgebras extending theN=1 supervirasoro algebra. This construction thus yields an infinite series of extended superconformal algebras.

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Communicated by N.Yu. Reshetikhin

Address after October 1991: Physikalisches Institut der Universität Bonn, FRG

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Figueroa-O'Farrill, J.M., Ramos, E. ClassicalN=1W-superalgebras from Hamiltonian reduction. Commun.Math. Phys. 145, 43–55 (1992). https://doi.org/10.1007/BF02099280

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