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Representation Theory

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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
MathSciNet review: 3163410
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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
MR Author ID: 845262

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