### Abstract

Original language | English |
---|---|

Pages (from-to) | 1-15 |

Number of pages | 15 |

Journal | Bulletin of the London Mathematical Society |

Volume | 41 |

Issue number | 1 |

Early online date | 26 Nov 2008 |

DOIs | |

Publication status | Published - Feb 2009 |

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### Cite this

*A*, and Richardson elements in seaweed Lie algebras.

*Bulletin of the London Mathematical Society*,

*41*(1), 1-15. https://doi.org/10.1112/blms/bdn087

**Rigid representations of a double quiver of type A, and Richardson elements in seaweed Lie algebras.** / Jensen, Bernt T; Su, Xiuping; Yu, Rupert Wei Tze.

Research output: Contribution to journal › Article

*A*, and Richardson elements in seaweed Lie algebras',

*Bulletin of the London Mathematical Society*, vol. 41, no. 1, pp. 1-15. https://doi.org/10.1112/blms/bdn087

}

TY - JOUR

T1 - Rigid representations of a double quiver of type A, and Richardson elements in seaweed Lie algebras

AU - Jensen, Bernt T

AU - Su, Xiuping

AU - Yu, Rupert Wei Tze

PY - 2009/2

Y1 - 2009/2

N2 - In this paper, we show that there is always an open adjoint orbit in the nilpotent radical of a seaweed Lie algebra in gln(k), thus answering positively in this gln(k) case to a question raised independently by Michel Duflo and Dmitri Panyushev. The proof gives an explicit construction, using �-filtered modules of quasi-hereditary algebras arising from quotients of the double of quivers of type A. An example of a seaweed Lie algebra in a simple Lie algebra of type E8 not admitting an open orbit in its nilpotent radical is given.

AB - In this paper, we show that there is always an open adjoint orbit in the nilpotent radical of a seaweed Lie algebra in gln(k), thus answering positively in this gln(k) case to a question raised independently by Michel Duflo and Dmitri Panyushev. The proof gives an explicit construction, using �-filtered modules of quasi-hereditary algebras arising from quotients of the double of quivers of type A. An example of a seaweed Lie algebra in a simple Lie algebra of type E8 not admitting an open orbit in its nilpotent radical is given.

UR - http://www.scopus.com/inward/record.url?scp=60749086817&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1112/blms/bdn087

U2 - 10.1112/blms/bdn087

DO - 10.1112/blms/bdn087

M3 - Article

VL - 41

SP - 1

EP - 15

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

SN - 0024-6093

IS - 1

ER -