Abstract
We establish the relation of BerensteinâKazhdan's decoration function and GrossâHackingâKeelâKontsevich's potential on the open double Bruhat cell in the base affine space G/N of a simple, simply connected, simply laced algebraic group G. As a byproduct we derive explicit identifications of polyhedral parametrization of canonical bases of the ring of regular functions on G/N arising from the tropicalizations of the potential and decoration function with the classical string and Lusztig parametrizations. In the appendix we construct maximal green sequences for the open double Bruhat cell in G/N which is a crucial assumption for GrossâHackingâKeelâKontsevich's construction.
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