Large chiral diffeomorphisms on Riemann surfaces and W-algebras

The diffeomorphism action lifted on truncated (chiral) Taylor expansion of acomplex scalar field over a Riemann surface is presented in the paper under thename of large diffeomorphisms. After an heuristic approach, we show how alinear truncation in the Taylor expansion can generate an algebra of symmetrycharacterized by some structure functions. Such a linear truncation isexplicitly realized by introducing the notion of Forsyth frame over the Riemannsurface with the help of a conformally covariant algebraic differentialequation. The large chiral diffeomorphism action is then implemented through aB.R.S. formulation (for a given order of truncation) leading to a morealgebraic set up. In this context the ghost fields behave as holomorphicallycovariant jets. Subsequently, the link with the so called W-algebras is madeexplicit once the ghost parameters are turned from jets into tensorial ghostones. We give a general solution with the help of the structure functionspertaining to all the possible truncations lower or equal to the given order.This provides another contribution to the relationship between KdV flows andW-diffeomorphimsComment: LaTeX file, 31 pages, no figure. Version to appear in J. Math. Phys. Work partly supported by Region PACA and INF