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arXiv · 1711.07176

Polyhedral parametrizations of canonical bases & cluster duality

Volker Genz·Gleb Koshevoy·Bea Schumann
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Abstract

We establish the relation of the potential function constructed by Gross-Hacking-Keel-Kontsevich's and Berenstein-Kazhdan's decoration function on the open double Bruhat cell in the base affine space $G/\mathcal{N}$ 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 $G/\mathcal{N}$ arising from the tropicalizations of the potential and decoration function with the classical string and Lusztig parametrizations.

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BibTeXRIS

Volker Genz, Gleb Koshevoy, Bea Schumann. 2017-11-20. Polyhedral parametrizations of canonical bases & cluster duality. https://arxiv.org/abs/1711.07176

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