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

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

2008-04-12

arxiv.org/abs/0804.2034v1

Mathematics

Quantum Algebra

Scientific paper

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

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