Nagoya Mathematical Journal

Determinant formulas for the {$\tau$}-functions of the Painlevé equations of type {$A$}

Yasuhiko Yamada

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Abstract

Explicit determinant formulas are presented for the $\tau$-functions of the generalized Painlevé equations of type $A$. This result allows an interpretation of the $\tau$-functions as the Plücker coordinates of the universal Grassmann manifold.

Article information

Source
Nagoya Math. J., Volume 156 (1999), 123-134.

Dates
First available in Project Euclid: 27 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1114631302

Mathematical Reviews number (MathSciNet)
MR1727896

Zentralblatt MATH identifier
1134.33325

Subjects
Primary: 34M55: Painlevé and other special equations; classification, hierarchies;
Secondary: 33E17: Painlevé-type functions 34M15: Algebraic aspects (differential-algebraic, hypertranscendence, group- theoretical) 37K35: Lie-Bäcklund and other transformations

Citation

Yamada, Yasuhiko. Determinant formulas for the {$\tau$}-functions of the Painlevé equations of type {$A$}. Nagoya Math. J. 156 (1999), 123--134. https://projecteuclid.org/euclid.nmj/1114631302


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References

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