Seminar in Representation Theory

主講者: | Ulrich Thiel (University of Kaiserslautern) |

講題: | Cellularity of endomorphism algebras of tilting objects |

時間: | 2021-08-27 (Fri.) 15:00 - 16:00 |

地點: | 數學所 演講廳(6F) (台大院區) |

Abstract: | We show that, in a highest weight category with duality, the endomorphism algebra of a tilting object is naturally a cellular algebra. Our proof generalizes a recent construction of Andersen,
Stroppel, and Tubbenhauer. This result raises the question of whether all cellular algebras can be realized in this way. The construction also
works without the presence of a duality and yields standard bases, in the sense of Du and Rui, which have similar combinatorial features to cellular bases. As an application, we obtain standard bases -- and thus a general theory of "cell modules" -- for Hecke algebras associated to finite complex reflection groups (as introduced by Broue, Malle, and Rouquier) via category O of the rational Cherednik algebra. For real reflection groups these bases are cellular.
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