On an analogue of the James conjecture

Williamson, Geordie

doi:10.1090/S1088-4165-2014-00447-3

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.

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