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In a categorification of tensor products of fundamental representations ofquantum sl(k) via highest weight categories, the indecomposable tilting modulesdescend to the canonical basis. Since projective functors map tilting modulesto tilting modules, the coefficients of the canonical basis of tensor productsof finite dimensional, irreducible representations under the action of theChevalley generators are positive.

Positivity and the canonical basis of tensor products of finite-dimensional irreducible representations of quantum sl(k)