### Abstract

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.

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 |

## Fingerprint Dive into the research topics of 'Rigid representations of a double quiver of type <em>A</em>, and Richardson elements in seaweed Lie algebras'. Together they form a unique fingerprint.

## Cite this

Jensen, B. T., Su, X., & Yu, R. W. T. (2009). Rigid representations of a double quiver of type

*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