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Representation Theory
Representation Theory
ISSN 1088-4165

 

On an analogue of the James conjecture


Author: Geordie Williamson
Journal: Represent. Theory 18 (2014), 15-27
MSC (2010): Primary 20C08, 20C20, 20C30
Published electronically: February 7, 2014
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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
Email: geordie@mpim-bonn.mpg.de

DOI: http://dx.doi.org/10.1090/S1088-4165-2014-00447-3
PII: S 1088-4165(2014)00447-3
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
Article copyright: © Copyright 2014 American Mathematical Society