Cluster Algebras and Representation Theory

被引：0

作者：

Leclerc, Bernard ^{[1
]}

机构：

[1] Univ Caen, CNRS UMR 6139, LMNO, F-14032 Caen, France

来源：

PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS, VOL IV: INVITED LECTURES | 2010年

关键词：

Cluster algebra; canonical and semicanonical basis; preprojective algebra; quantum affine algebra; FINITE-DIMENSIONAL REPRESENTATIONS; SEMICANONICAL BASES; QUIVER VARIETIES; Q-CHARACTERS; CATEGORIES; SYSTEMS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We apply the new theory of cluster algebras of Fomin and" Zelevinsky to study some combinatorial problems arising in Lie theory. This is joint work with Geiss and Schroer (3, 4, 5, 6), and with Hernandez (8, 9).

引用

页码：2471 / 2488

页数：18

共 53 条

[11]

Chari V., 1994, A Guide to Quantum Groups

[12] On the exceptional fibres of Kleinian singularities [J].

Crawley-Boevey, W .

AMERICAN JOURNAL OF MATHEMATICS, 2000, 122 (05) :1027-1037

[13]

Derksen H., J AM MATH S IN PRESS

[14] Quivers with potentials and their representations I: Mutations [J].

Derksen, Harm ;

Weyman, Jerzy ;

Zelevinsky, Andrei .

SELECTA MATHEMATICA-NEW SERIES, 2008, 14 (01) :59-119

[15] Q-systems as Cluster Algebras II: Cartan Matrix of Finite Type and the Polynomial Property [J].

Di Francesco, Philippe ;

Kedem, Rinat .

LETTERS IN MATHEMATICAL PHYSICS, 2009, 89 (03) :183-216

[16] Y-systems and generalized associahedra [J].

Fomin, S ;

Zelevinsky, A .

ANNALS OF MATHEMATICS, 2003, 158 (03) :977-1018

[17] Cluster algebras II: Finite type classification [J].

Fomin, S ;

Zelevinsky, A .

INVENTIONES MATHEMATICAE, 2003, 154 (01) :63-121

[18] Cluster algebras I: Foundations [J].

Fomin, S ;

Zelevinsky, A .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 15 (02) :497-529

[19]

Fomin S., 2010, P INT C MATH HYD

[20] Cluster algebras IV: Coefficients [J].

Fomin, Sergey ;

Zelevinsky, Andrei .

COMPOSITIO MATHEMATICA, 2007, 143 (01) :112-164

← 1 2 3 4 5 6 →