dorsal/arxiv
View SchemaNonstandard Drinfeld-Sokolov reduction
| Authors | F. Delduc, L. Feher, L. Gallot |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9708002 |
| URL | https://arxiv.org/abs/solv-int/9708002 |
| DOI | 10.1088/0305-4470/31/25/006 |
Abstract
Subject to some conditions, the input data for the Drinfeld-Sokolov construction of KdV type hierarchies is a quadruplet $(\A,\Lambda, d_1, d_0)$, where the $d_i$ are $\Z$-gradations of a loop algebra $\A$ and $\Lambda\in \A$ is a semisimple element of nonzero $d_1$-grade. A new sufficient condition on the quadruplet under which the construction works is proposed and examples are presented. The proposal relies on splitting the $d_1$-grade zero part of $\A$ into a vector space direct sum of two subalgebras. This permits one to interpret certain Gelfand-Dickey type systems associated with a nonstandard splitting of the algebra of pseudo-differential operators in the Drinfeld-Sokolov framework.
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"abstract": "Subject to some conditions, the input data for the Drinfeld-Sokolov\nconstruction of KdV type hierarchies is a quadruplet $(\\A,\\Lambda, d_1, d_0)$,\nwhere the $d_i$ are $\\Z$-gradations of a loop algebra $\\A$ and $\\Lambda\\in \\A$\nis a semisimple element of nonzero $d_1$-grade. A new sufficient condition on\nthe quadruplet under which the construction works is proposed and examples are\npresented. The proposal relies on splitting the $d_1$-grade zero part of $\\A$\ninto a vector space direct sum of two subalgebras. This permits one to\ninterpret certain Gelfand-Dickey type systems associated with a nonstandard\nsplitting of the algebra of pseudo-differential operators in the\nDrinfeld-Sokolov framework.",
"arxiv_id": "solv-int/9708002",
"authors": [
"F. Delduc",
"L. Feher",
"L. Gallot"
],
"categories": [
"solv-int",
"hep-th",
"nlin.SI"
],
"doi": "10.1088/0305-4470/31/25/006",
"title": "Nonstandard Drinfeld-Sokolov reduction",
"url": "https://arxiv.org/abs/solv-int/9708002"
},
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