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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.


Rationality of blocks of quasi-simple finite groups
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by Niamh Farrell and Radha Kessar
Represent. Theory 23 (2019), 325-349
Published electronically: September 30, 2019


Let $\ell$ be a prime number. We show that the Morita Frobenius number of an $\ell$-block of a quasi-simple finite group is at most $4$ and that the strong Frobenius number is at most $4 |D|^2!$, where $D$ denotes a defect group of the block. We deduce that a basic algebra of any block of the group algebra of a quasi-simple finite group over an algebraically closed field of characteristic $\ell$ is defined over a field with $\ell ^a$ elements for some $a \leq 4$. We derive consequences for Donovan’s conjecture. In particular, we show that Donovan’s conjecture holds for $\ell$-blocks of special linear groups.
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Bibliographic Information
  • Niamh Farrell
  • Affiliation: Fachbereich Mathematik, TU Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany
  • Email:
  • Radha Kessar
  • Affiliation: Department of Mathematics, City, University of London, Northampton Square, EC1V 0HB London, United Kingdom
  • MR Author ID: 614227
  • Email:
  • Received by editor(s): July 4, 2018
  • Received by editor(s) in revised form: May 24, 2019
  • Published electronically: September 30, 2019
  • Additional Notes: This article was partly written while the authors were visiting the Mathematical Sciences Research Institute in Berkeley, California in Spring 2018 for the programme Group Representation Theory and Applications supported by the National Science Foundation under Grant No. DMS-1440140.
    The first author also gratefully acknowledges financial support from the DFG project SFB-TRR 195
  • © Copyright 2019 American Mathematical Society
  • Journal: Represent. Theory 23 (2019), 325-349
  • MSC (2010): Primary 20C20; Secondary 20C33
  • DOI:
  • MathSciNet review: 4013115