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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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A new construction of the asymptotic algebra associated to the $q$-Schur algebra
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by Olivier Brunat and Max Neunhöffer PDF
Represent. Theory 16 (2012), 88-107 Request permission


We denote by $A$ the ring of Laurent polynomials in the indeterminate $v$ and by $K$ its field of fractions. In this paper, we are interested in representation theory of the “generic” $q$-Schur algebra $\mathcal {S}_q(n,r)$ over $A$. We will associate to every symmetrising trace form $\tau$ on $K\mathcal {S}_q(n,r)$ a subalgebra $\mathcal {J}_{\tau }$ of $K\mathcal {S}_q(n,r)$ which is isomorphic to the “asymptotic” algebra $\mathcal {J}(n,r)_A$ defined by J. Du. As a consequence, we give a new hypothesis which implies James’ conjecture.
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Additional Information
  • Olivier Brunat
  • Affiliation: Ruhr-Universität Bochum, Fakultät für Mathematik, D-44780 Bochum, Germany
  • Address at time of publication: Institut de Mathèmatiques de Jussieu, UFR de Mathèmatiques, 175, rue du Chevaleret, F-75013 Paris
  • Email:
  • Max Neunhöffer
  • Affiliation: School of Mathematics and Statistics, Mathematical Institute, North Haugh, St Andrews, Fife KY16 9SS, Scotland, United Kingdom
  • Email:
  • Received by editor(s): January 9, 2009
  • Received by editor(s) in revised form: April 2, 2010
  • Published electronically: January 18, 2012
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 16 (2012), 88-107
  • MSC (2010): Primary 20C08, 20F55; Secondary 20G05
  • DOI:
  • MathSciNet review: 2869019