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 |
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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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