dorsal/arxiv
View SchemaThe Constrained KP Hierarchy and the Generalised Miura Transformation
| Authors | Javier Mas, Eduardo Ramos |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9501009 |
| URL | https://arxiv.org/abs/q-alg/9501009 |
| DOI | 10.1016/0370-2693(95)00357-Q |
Abstract
Recently much attention has been paid to the restriction of KP to the submanifold of operators which can be represented as a ratio of two purely differential operators L=AB^{-1}. Whereas most of the aspects concerning this reduced hierarchy, like the Lax flows and the Hamiltonians, are by now well understood, there still lacks a clear and conclusive statement about the associated Poisson structure. We fill this gap by placing the problem in a more general framework and then showing how the required result follows from an interesting property of the second Gelfand-Dickey brackets under multiplication and inversion of Lax operators. As a byproduct we give an elegant and simple proof of the generalised Kupershmidt-Wilson theorem.
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"abstract": "Recently much attention has been paid to the restriction of KP to the\nsubmanifold of operators which can be represented as a ratio of two purely\ndifferential operators L=AB^{-1}. Whereas most of the aspects concerning this\nreduced hierarchy, like the Lax flows and the Hamiltonians, are by now well\nunderstood, there still lacks a clear and conclusive statement about the\nassociated Poisson structure. We fill this gap by placing the problem in a more\ngeneral framework and then showing how the required result follows from an\ninteresting property of the second Gelfand-Dickey brackets under multiplication\nand inversion of Lax operators. As a byproduct we give an elegant and simple\nproof of the generalised Kupershmidt-Wilson theorem.",
"arxiv_id": "q-alg/9501009",
"authors": [
"Javier Mas",
"Eduardo Ramos"
],
"categories": [
"q-alg",
"hep-th",
"math.QA"
],
"doi": "10.1016/0370-2693(95)00357-Q",
"title": "The Constrained KP Hierarchy and the Generalised Miura Transformation",
"url": "https://arxiv.org/abs/q-alg/9501009"
},
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