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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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On an analogue of the James conjecture
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by Geordie Williamson PDF
Represent. Theory 18 (2014), 15-27 Request permission

Abstract:

We give a counterexample to the most optimistic analogue (due to Kleshchev and Ram) of the James conjecture for Khovanov-Lauda-Rouquier algebras associated to simply-laced Dynkin diagrams. The first counterexample occurs in type $A_5$ for $p = 2$ and involves the same singularity used by Kashiwara and Saito to show the reducibility of the characteristic variety of an intersection cohomology $D$-module on a quiver variety. Using recent results of Polo one can give counterexamples in type $A$ in all characteristics.
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Additional Information
  • Geordie Williamson
  • Affiliation: Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
  • MR Author ID: 845262
  • Email: geordie@mpim-bonn.mpg.de
  • Received by editor(s): April 4, 2013
  • Received by editor(s) in revised form: May 10, 2013, and October 2, 2013
  • Published electronically: February 7, 2014

  • Dedicated: Dedicated to Jimi
  • © Copyright 2014 American Mathematical Society
  • Journal: Represent. Theory 18 (2014), 15-27
  • MSC (2010): Primary 20C08, 20C20, 20C30
  • DOI: https://doi.org/10.1090/S1088-4165-2014-00447-3
  • MathSciNet review: 3163410