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Let $\mathfrak g$ be a semi-simple Lie algebra (We can assume $\mathfrak g=sl(n)$ for simplicity) and let $O_q(\mathfrak g)$ be the corresponding quantum algebra of functions. Then $O_q(\mathfrak g)^{\...

I am trying to understand the canonical basis of quantum groups and different ways to construct the canonical basis of quantum groups. In the comments of Lusztig's papers, the paper [92], CANONICAL ...

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 ...

I've heard asserted in talks quite a few times that Lusztig's canonical basis for irreducible representations is known to not always have positive structure coefficents for the action of $E_i$ and $...