dorsal/arxiv
View SchemaSymmetries in the fourth Painleve equation and Okamoto polynomials
| Authors | Masatoshi Noumi, Yasuhiko Yamada |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9708018 |
| URL | https://arxiv.org/abs/q-alg/9708018 |
Abstract
We propose a new representation of the fourth Painlev\'e equation in which the $A^{(1)}_2$-symmetries become clearly visible. By means of this representation, we clarify the internal relation between the fourth Painlev\'e equation and the modified KP hierarchy. We obtain in particular a complete description of the rational solutions of the fourth Painlev\'e equation in terms of Schur functions. This implies that the so-called Okamoto polynomials, which arise from the $\tau$-functions for rational solutions, are in fact expressible by the 3-reduced Schur functions.
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"abstract": "We propose a new representation of the fourth Painlev\\\u0027e equation in which\nthe $A^{(1)}_2$-symmetries become clearly visible. By means of this\nrepresentation, we clarify the internal relation between the fourth Painlev\\\u0027e\nequation and the modified KP hierarchy. We obtain in particular a complete\ndescription of the rational solutions of the fourth Painlev\\\u0027e equation in\nterms of Schur functions. This implies that the so-called Okamoto polynomials,\nwhich arise from the $\\tau$-functions for rational solutions, are in fact\nexpressible by the 3-reduced Schur functions.",
"arxiv_id": "q-alg/9708018",
"authors": [
"Masatoshi Noumi",
"Yasuhiko Yamada"
],
"categories": [
"q-alg",
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"title": "Symmetries in the fourth Painleve equation and Okamoto polynomials",
"url": "https://arxiv.org/abs/q-alg/9708018"
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