dorsal/arxiv
View SchemaBispectral Operators of Rank 1 and Dual Isomonodromic Deformations
| Authors | J. Harnad |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9612012 |
| URL | https://arxiv.org/abs/solv-int/9612012 |
| Journal | CRM Proc. Lecture Notes 11, 155-167 (Amer. Math. Soc., Providence RI, 1997) |
Abstract
A comparison is made between bispectral operator pairs and dual pairs of isomonodromic deformation equations. Through examples, it is shown how operators belonging to rank one bispectral algebras may be viewed equivalently as defining 1-parameter families of rational first order differential operators with matricial coefficients on the Riemann sphere, whose monodromy is trivial. By interchanging the r\^oles of the two variables entering in the bispectral pair, a second 1-parameter family of operators with trivial monodromy is obtained, which may be viewed as the dual isomonodromic deformation system.
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"abstract": "A comparison is made between bispectral operator pairs and dual pairs of\nisomonodromic deformation equations. Through examples, it is shown how\noperators belonging to rank one bispectral algebras may be viewed equivalently\nas defining 1-parameter families of rational first order differential operators\nwith matricial coefficients on the Riemann sphere, whose monodromy is trivial.\nBy interchanging the r\\^oles of the two variables entering in the bispectral\npair, a second 1-parameter family of operators with trivial monodromy is\nobtained, which may be viewed as the dual isomonodromic deformation system.",
"arxiv_id": "solv-int/9612012",
"authors": [
"J. Harnad"
],
"categories": [
"solv-int",
"hep-th",
"nlin.SI"
],
"journal_ref": "CRM Proc. Lecture Notes 11, 155-167 (Amer. Math. Soc., Providence\n RI, 1997)",
"title": "Bispectral Operators of Rank 1 and Dual Isomonodromic Deformations",
"url": "https://arxiv.org/abs/solv-int/9612012"
},
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