ABSTRACT: (Joint work with M. Reineke (Wuppertal)). We consider the link between the combinatorics of the canonical basis of a quantized enveloping algebra and the monomial bases of M. Reineke arising from representations of quivers. It will be seen how some reparametrization functions of the canonical basis, arising from the link between Lusztig's approach to the canonical basis and the string parametrization of the canonical basis, are given on a large region of linearity by linear functions arising from these monomial bases for a quantized enveloping algebra.

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