Questions about the Khovanov-Lauda-Rouquier algebras. These algebras are used in particular to categorify the representations of universal enveloping algebras of semi-simple Lie algebras

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Where does the canonical basis differ from the KLR basis?

The question implicitly asked in Ben Webster's question is: Does the canonical basis of Uq(n+) agree with the basis coming from categorification via Khovanov-Lauda-Rouqier algebras? Thanks to ...
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Are cyclotomic Khovanov-Lauda-Rouquier algebras symmetric?

Recall that for k a field, a finite dimensional k-algebra A is called symmetric if it is isomorphic to its dual as a bimodule of itself. Which is to say, there's a trace map t:A -> k such that ...