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Balanced semisimple filtrations for tilting modules

Hazi, A. ORCID: 0000-0001-7264-2211 (2017). Balanced semisimple filtrations for tilting modules. Representation Theory, 21(2), pp. 4-19. doi: 10.1090/ert/495


Let Ul be a quantum group at an lth root of unity, obtained via Lusztig's divided powers construction. Many indecomposable tilting modules for Ul have been shown to have what we call a balanced semisimple filtration, or a Loewy series whose semisimple layers are symmetric about some middle layer. The existence of such filtrations suggests a remarkably straight-forward algorithm for calculating these characters if the irreducible characters are already known. We first show that the results of this algorithm agree with
Soergel's character formula for the regular indecomposable tilting modules. We then show that these balanced semisimple filtrations really do exist for
these tilting modules.

Publication Type: Article
Additional Information: © Copyright 2017 American Mathematical Society. First published in Representation Theory in Volume 21, 2017, published by the American Mathematical Society
Publisher Keywords: 0101 Pure Mathematics
Departments: School of Science & Technology > Mathematics
SWORD Depositor:
Text - Accepted Version
Available under License Creative Commons Attribution Non-commercial No Derivatives.

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