Polyhedral parametrizations of canonical bases & cluster duality

被引：8

作者：

Genz, Volker ^{[1
]}

Koshevoy, Gleb ^{[2
,3
]}

Schumann, Bea ^{[4
]}

机构：

[1] Ruhr Univ Bochum, Fac Math, Univ Str 150, D-44801 Bochum, Germany

[2] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow, Russia

[3] Natl Res Univ Higher Sch Econ, Moscow, Russia

[4] Univ Cologne, Math Inst, Cologne, Germany

来源：

ADVANCES IN MATHEMATICS | 2020年 / 369卷

关键词：

Cluster algebras; Quantum groups; Canonical bases; Mirror symmetry; TORIC DEGENERATIONS; FLAG;

D O I：

10.1016/j.aim.2020.107178

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：41

共 38 条

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Alexeev V., 2004, SELECTA MATH, V10, P453

[2]