Symmetries in the fourth Painleve equation and Okamoto polynomials

1997/08/19 by Noumi, Masatoshi, Yamada, Yasuhiko
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.q-alg/9708018

Abstract

We propose a new representation of the fourth Painlevé equation in which the A⁽¹⁾₂-symmetries become clearly visible. By means of this representation, we clarify the internal relation between the fourth Painlevé equation and the modified KP hierarchy. We obtain in particular a complete description of the rational solutions of the fourth Painlevé equation in terms of Schur functions. This implies that the so-called Okamoto polynomials, which arise from the τ-functions for rational solutions, are in fact expressible by the 3-reduced Schur functions.

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