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Representation Theory

ISSN 1088-4165



Balanced semisimple filtrations for tilting modules

Author: Amit Hazi
Journal: Represent. Theory 21 (2017), 4-19
MSC (2010): Primary 20G42
Published electronically: March 8, 2017
MathSciNet review: 3620676
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Abstract: Let $U_l$ be a quantum group at an $l$th root of unity, obtained via Lusztig’s 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 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.

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Amit Hazi
Affiliation: Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, United Kingdom

Received by editor(s): October 11, 2016
Received by editor(s) in revised form: February 15, 2017
Published electronically: March 8, 2017
Article copyright: © Copyright 2017 American Mathematical Society