The cluster and dual canonical bases of Z[x(11), ..., x(33)] are equal

Brendon Rhoades
2010 Discrete Mathematics & Theoretical Computer Science  
Combinatorics International audience 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.
doi:10.46298/dmtcs.515 fatcat:jha52xpfwzhz7hyzconw7fq2xm