### Abstract

The Drinfeld-Sokolov reduction method has been used to associate extensions of the matrix r-KdV system with the Lie algebra gl_{n}. We present reductions of these systems to the fixed point sets of involutive Poisson maps, implementing the reduction of gl_{n} to classical Lie algebras of type B, C, D. Modifications corresponding, in the first place to factorization of the Lax operator, and then to Wakimoto realizations of the current algebra components of the factorization, are also described.

Original language | English |
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Pages (from-to) | 5815-5824 |

Number of pages | 10 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 30 |

Issue number | 16 |

DOIs | |

Publication status | Published - Aug 21 1997 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Physics A: Mathematical and General*,

*30*(16), 5815-5824. https://doi.org/10.1088/0305-4470/30/16/022

**Extended matrix Gelfand-Dickey hierarchies : Reduction to classical Lie algebras.** / Fehér, László; Marshall, Ian.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 30, no. 16, pp. 5815-5824. https://doi.org/10.1088/0305-4470/30/16/022

}

TY - JOUR

T1 - Extended matrix Gelfand-Dickey hierarchies

T2 - Reduction to classical Lie algebras

AU - Fehér, László

AU - Marshall, Ian

PY - 1997/8/21

Y1 - 1997/8/21

N2 - The Drinfeld-Sokolov reduction method has been used to associate extensions of the matrix r-KdV system with the Lie algebra gln. We present reductions of these systems to the fixed point sets of involutive Poisson maps, implementing the reduction of gln to classical Lie algebras of type B, C, D. Modifications corresponding, in the first place to factorization of the Lax operator, and then to Wakimoto realizations of the current algebra components of the factorization, are also described.

AB - The Drinfeld-Sokolov reduction method has been used to associate extensions of the matrix r-KdV system with the Lie algebra gln. We present reductions of these systems to the fixed point sets of involutive Poisson maps, implementing the reduction of gln to classical Lie algebras of type B, C, D. Modifications corresponding, in the first place to factorization of the Lax operator, and then to Wakimoto realizations of the current algebra components of the factorization, are also described.

UR - http://www.scopus.com/inward/record.url?scp=0031582699&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031582699&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/30/16/022

DO - 10.1088/0305-4470/30/16/022

M3 - Article

VL - 30

SP - 5815

EP - 5824

JO - Journal Physics D: Applied Physics

JF - Journal Physics D: Applied Physics

SN - 0022-3727

IS - 16

ER -