Cluster algebras and semi-invariant rings I. Triple flags

被引：5

作者：

Fei, Jiarui ^{[1
]}

机构：

[1] Shanghai Jiao Tong Univ, Dept Math, Dongchuan Rd 800, Shanghai 200240, Peoples R China

来源：

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY | 2017年 / 115卷

关键词：

13F60; 16G20 (primary); 13A50; 52B20 (secondary); QUIVERS; REPRESENTATIONS; COMBINATORICS; COEFFICIENTS; POTENTIALS; SATURATION; VARIETIES; BASES;

D O I：

10.1112/plms.12033

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that each semi-invariant ring of the complete triple flag of length n is an upper cluster algebra associated to an ice hive quiver. We find a rational polyhedral cone Gn such that the generic cluster character maps its lattice points onto a basis of the upper cluster algebra. As an application, we use the cluster algebra structure to find a special minimal set of generators for these semi-invariant rings when n is small.

引用

页码：1 / 32

页数：32