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 |

Sample Search Hits | Sample Images | Cited Works

…x29; when λ is a
hook.
Affine *Cellularity* of KLR Algebras of Finite Types
The content of chapter II has already been published as (18). The goal of
chapter II is to establish (graded) affine *cellularity* in the sense of Koenig and Xi…

…graded) *cellularity* of cyclotomic KLR algebras of finite types.
Our approach is independent of the homological results in (30), (13) and (3)
(which relies on (30)). The connection between the theory…

…*cellularity*. We begin in subsection 2.2 by choosing
some special word idempotents and proving some properties they enjoy.
Subsection 2.2 introduces the notation that allows us to define our affine cellular
structure. This subsection also contains the crucial…

…Specht module S µ to S λ , where λ is a hook. In
section 6, we consider some examples.
10
CHAPTER II
AFFINE *CELLULARITY* OF KLR ALGEBRAS
The content of this chapter has already been published as (18).
Preliminaries and a Dimension Formula
In…