## On an analogue of the James conjecture

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- by Geordie Williamson
- Represent. Theory
**18**(2014), 15-27 - DOI: https://doi.org/10.1090/S1088-4165-2014-00447-3
- 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.## References

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## Bibliographic 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
- © 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

Dedicated: Dedicated to Jimi