The polynomial ring Z[x(11), ..., x(33)] has a basis called the dual canonical basis whose quantization facilitates the study of representations of the quantum group U-q(sl(3) (C)). On the other hand, Z[x(1 1), ... , x(33)] inherits a basis from the cluster monomial basis of a geometric model of the type D-4 cluster algebra. We prove that these two bases are equal. This extends work of Skandera and proves a conjecture of Fomin and Zelevinsky.

Source : oai:HAL:hal-00990455v1

Volume: Vol. 12 no. 5

Section: Combinatorics

Published on: January 1, 2010

Submitted on: March 26, 2015

Keywords: quantum group,cluster algebra,canonical basis,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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