## Balanced semisimple filtrations for tilting modules

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- by Amit Hazi
- Represent. Theory
**21**(2017), 4-19 - DOI: https://doi.org/10.1090/ert/495
- Published electronically: March 8, 2017
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## Abstract:

Let $U_l$ be a quantum group at an $l$th root of unity, obtained via Lusztigโs divided powers construction. Many indecomposable tilting modules for $U_l$ 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 straightforward algorithm for calculating these characters if the irreducible characters are already known. We first show that the results of this algorithm agree with Soergelโs character formula for the regular indecomposable tilting modules. We then show that these balanced semisimple filtrations really do exist for these tilting modules.

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## Bibliographic Information

**Amit Hazi**- Affiliation: Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, United Kingdom
- Email: A.Hazi@dpmms.cam.ac.uk
- Received by editor(s): October 11, 2016
- Received by editor(s) in revised form: February 15, 2017
- Published electronically: March 8, 2017
- © Copyright 2017 American Mathematical Society
- Journal: Represent. Theory
**21**(2017), 4-19 - MSC (2010): Primary 20G42
- DOI: https://doi.org/10.1090/ert/495
- MathSciNet review: 3620676