Full Record

Author | Loubert, Joseph |

Title | Affine Cellularity of Finite Type KLR Algebras, and Homomorphisms Between Specht Modules for KLR Algebras in Affine Type A |

URL | http://hdl.handle.net/1794/19255 |

Publication Date | 2015 |

Date Accessioned | 2015-08-18 23:02:53 |

Degree | PhD |

Discipline/Department | Department of Mathematics |

Degree Level | doctoral |

University/Publisher | University of Oregon |

Abstract | This thesis consists of two parts. In the first we prove that the Khovanov-Lauda-Rouquier algebras $R_\alpha$ of finite type are (graded) affine cellular in the sense of Koenig and Xi. In fact, we establish a stronger property, namely that the affine cell ideals in $R_\alpha$ are generated by idempotents. This in particular implies the (known) result that the global dimension of $R_\alpha$ is finite. In the second part we use the presentation of the Specht modules given by Kleshchev-Mathas-Ram to derive results about Specht modules. In particular, we determine all homomorphisms from an arbitrary Specht module to a fixed Specht module corresponding to any hook partition. Along the way, we give a complete description of the action of the standard KLR generators on the hook Specht module. This work generalizes a result of James. This dissertation includes previously published coauthored material. |

Subjects/Keywords | Affine cellularity; KLR algebras; Specht modules |

Contributors | Kleshchev, Alexander (advisor) |

Language | en |

Rights | Creative Commons BY 4.0-US [Always confirm rights and permissions with the source record.] |

Country of Publication | us |

Record ID | handle:1794/19255 |

Repository | oregon |

Date Retrieved | 2020-06-15 |

Date Indexed | 2020-06-18 |

Grantor | University of Oregon |

Issued Date | 2015-08-18 00:00:00 |