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POINT CONFIGURATIONS, CREMONA TRANSFORMATIONS AND THE ELLIPTIC DIFFERENCE PAINLEVE EQUATION
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- Kajiwara, Kenji
- Graduate School of Mathematics, Kyushu University
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- Masuda, Tetsu
- Department of Mathematics, Kobe University
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- Noumi, Masatoshi
- Department of Mathematics, Kobe University
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- Ohta, Yasuhiro
- Department of Mathematics, Kobe University
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- Yamada, Yasuhiko
- Department of Mathematics, Kobe University
Description
A theoretical foundation for a generalization of the elliptic difference Painleve 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 $ \tau $-functions is developed to translate it into a system of bilinear equations of Hirota-Miwa type for the $ \tau $-functions on the lattice. Application of this approach is also discussed to the elliptic difference Painleve equation.
Journal
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- MHF Preprint Series
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MHF Preprint Series 2005-5 2005-02-01
Faculty of Mathematics, Kyushu University