Cellularity of endomorphism algebras of tilting objects

Bellamy, G. and Thiel, U. (2022) Cellularity of endomorphism algebras of tilting objects. Advances in Mathematics, 404(Part A), 108387. (doi: 10.1016/j.aim.2022.108387)

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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 [4]. 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 Broué, Malle, and Rouquier) via category O of the rational Cherednik algebra. For real reflection groups these bases are cellular.

Item Type:Articles
Additional Information:The first author was partially supported by EPSRC grant EP/N005058/1. The second author was partially supported by the DFG SPP 1489, by a Research Support Fund from the Edinburgh Mathematical Society, and by the Australian Research Council Discovery Projects grant no. DP160103897.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Bellamy, Professor Gwyn
Authors: Bellamy, G., and Thiel, U.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Advances in Mathematics
Publisher:Elsevier
ISSN:0001-8708
ISSN (Online):1090-2082
Published Online:26 April 2022
Copyright Holders:Copyright © 2022 Elsevier Inc.
First Published:First published in Advances in Mathematics 404(Part A): 108387
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
171924Symplectic representation theoryGwyn BellamyEngineering and Physical Sciences Research Council (EPSRC)EP/N005058/1M&S - Mathematics