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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 | Abstract: | 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 $ 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 | Services: | Forum | Review | PDF | Favorites |
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