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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Balanced semisimple filtrations for tilting modules
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by Amit Hazi
Represent. Theory 21 (2017), 4-19
Published electronically: March 8, 2017


Let $U_l$ be a quantum group at an $l$th root of unity, obtained via Lusztigโ€™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 Soergelโ€™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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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:
  • 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:
  • MathSciNet review: 3620676