Canonical basis linearity regions arising from quiver representations

Details Canonical basis linearity regions arising from quiver representations Canonical basis linearity regions arising from quiver representations

2002-09-16

arxiv.org/abs/math/0209188v1

Mathematics

Quantum Algebra

30 pages

Scientific paper

In this paper we show that there is a link between the combinatorics of the canonical basis of a quantized enveloping algebra and the monomial bases of the second author arising from representations of quivers. We prove that 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 basis for a quantized enveloping algebra.

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