## A quiver presentation for Solomon's descent algebra

dc.contributor.author | Pfeiffer, Götz | en |

dc.date.accessioned | 2010-01-18T19:42:47Z | en |

dc.date.available | 2010-01-18T19:42:47Z | en |

dc.date.issued | 2009 | en |

dc.identifier.citation | Pfeiffer G. (2009),A quiver presentation for Solomon's descent algebra. "Advances in Mathematics", 220 (5)1428-1465 | en |

dc.identifier.uri | http://hdl.handle.net/10379/600 | en |

dc.description.abstract | The descent algebra S(W) is a subalgebra of the group algebra of a finite Coxeter group W, which supports a homomorphism with nilpotent kernel and commutative image in the character ring of W. Thus S(W) is a basic algebra, and as such it has a presentation as a quiver with relations. Here we construct S(W) as a quotient of a subalgebra of the path algebra of the Hasse diagram of the Boolean lattice of all subsets of S, the set of simple reflections in W. From this construction we obtain some general information about the quiver of S(W) and an algorithm for the construction of a quiver presentation for the descent algebra S(W) of any given finite Coxeter group W. | en |

dc.format | application/pdf | en |

dc.language.iso | en | en |

dc.publisher | Elsvier | en |

dc.subject | Finite Coxeter group | en |

dc.subject | Descent algebra | en |

dc.subject | Quiver presentation | en |

dc.title | A quiver presentation for Solomon's descent algebra | en |

dc.type | Article | en |

dc.local.publishedsource | http://dx.doi.org/10.1016/j.aim.2008.11.005 | en |

dc.description.peer-reviewed | peer-reviewed | en |

nui.item.downloads | 490 |

### Files in this item

This item is available under the Attribution-NonCommercial-NoDerivs 3.0 Ireland. No item may be reproduced for commercial purposes. Please refer to the publisher's URL where this is made available, or to notes contained in the item itself. Other terms may apply.

The following license files are associated with this item: