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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Rationality of blocks of quasi-simple finite groups
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by Niamh Farrell and Radha Kessar PDF
Represent. Theory 23 (2019), 325-349 Request permission

Abstract:

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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Additional Information
  • Niamh Farrell
  • Affiliation: Fachbereich Mathematik, TU Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany
  • Email: farrell@mathematik.uni-kl.de
  • Radha Kessar
  • Affiliation: Department of Mathematics, City, University of London, Northampton Square, EC1V 0HB London, United Kingdom
  • MR Author ID: 614227
  • Email: radha.kessar.1@city.ac.uk
  • 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: https://doi.org/10.1090/ert/530
  • MathSciNet review: 4013115