ar X iv : n lin / 0 41 10 03 v 1 [ nl in . S I ] 2 N ov 2 00 4 Point configurations , Cremona transformations and the elliptic difference Painlevé equation
نویسندگان
چکیده
A theoretical foundation for a generalization of the elliptic difference Painlevé equation to higher dimensions is provided in the framework of birational Weyl group action on the space of point configurations in general position in a projective space. By introducing an elliptic parametrization of point configurations, a realization of the Weyl group is proposed as a group of Cremona transformations containing elliptic functions in the coefficients. For this elliptic Cremona system, a theory of τ-functions is developed to translate it into a system of bilinear equations of Hirota-Miwa type for the τ-functions on the lattice. Application of this approach is also discussed to the elliptic difference Painlevé equation.
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