Polyhedral parametrizations of canonical bases & cluster duality
Polyhedral parametrizations of canonical bases & cluster duality
复制标题
规范基的多面体参数化
DOI：
10.1016/j.aim.2020.107178
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发表时间：
2017
影响因子：
1.7
通讯作者：
Bea Schumann
中科院分区：
文献类型：
--
作者：
Volker Genz;G. Koshevoy;Bea Schumann
建立了单连通单缀代数群G的基仿射空间G/N中开双Bruhat胞腔上的Berenstein-Kazhdan装饰函数与Gross-Hacking-Keel-Kontsevich势之间的关系。作为一个副产品，我们得到明确的标识多面体参数化的正则函数的G/N环的正则基所产生的潜在的热带化和装饰功能与经典的字符串和Lusztig参数化。在附录中，我们构造了G/N中开双Bruhat胞腔的极大绿色序列，这是Gross-Hacking-Keel-Kontsevich构造的一个重要假设。
We establish the relation of Berenstein–Kazhdan's decoration function and Gross–Hacking–Keel–Kontsevich'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 Gross–Hacking–Keel–Kontsevich's construction.