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Determinant formulas for the $τ$-functions of the Painlevé equations of type $A$

Yasuhiko Yamada
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Abstract

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

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BibTeXRIS

Yasuhiko Yamada. 1998-08-03. Determinant formulas for the $τ$-functions of the Painlevé equations of type $A$. https://arxiv.org/abs/math/9808002

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