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Symmetries, Lax pair, and nilpotent Darboux transformation for the KdV-ghost system
We analyze the KdV--ghost system arising from the BRST formulation of BF-type topological field theory, its symmetries, Lax pair, spectral problem, zero-curvature formulation and Darboux formalism. The system is invariant under shifts of the ghost field, whose generator does not commute with the BRS
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