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28 March 2024
 
  » arxiv » nlin.SI/0411003

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Point configurations, Cremona transformations and the elliptic difference Painlevé equation
K.Kajiwara ; T.Masuda ; M.Noumi ; Y.Ohta ; Y.Yamada ;
Date 2 Nov 2004
Subject Exactly Solvable and Integrable Systems; Algebraic Geometry | nlin.SI math.AG
AbstractA 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 $ au$-functions is developed to translate it into a system of bilinear equations of Hirota-Miwa type for the $ au$-functions on the lattice.
Source arXiv, nlin.SI/0411003
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