Tensor diagrams and cluster algebras

被引：24

作者：

Fomin, Sergey ^{[1
]}

Pylyayskyy, Pavlo ^{[2
]}

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[2] Univ Minnesota, Dept Math, Minneapolis, MN 55414 USA

来源：

ADVANCES IN MATHEMATICS | 2016年 / 300卷

基金：

美国国家科学基金会;

关键词：

Cluster algebra; Invariant theory; Web basis; Tensor diagram; SEMICANONICAL BASES; QUIVER VARIETIES; POSITIVITY; FINITE;

D O I：

10.1016/j.aim.2016.03.030

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The rings of SL(V) invariants of configurations of vectors and linear forms in a finite-dimensional complex vector space V were explicitly described by Hermann Weyl in the 1930s. We show that when. V is 3-dimensional, each of these rings carries a natural cluster algebra structure (typically, many of them) whose cluster variables include Weyl's generators. We describe and explore these cluster structures using the combinatorial machinery of tensor diagrams. A key role is played by the web bases introduced by G. Kuperberg. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：717 / 787

页数：71

共 55 条

[1] Brill-Gordan loci, transvectants and an analogue of the Foulkes conjecture [J].