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
收藏
页码:2471 / 2488
页数:18
相关论文
共 53 条
[1]  
[Anonymous], SEMINAIRE BOURBAKI E
[2]  
[Anonymous], 1998, Algebras and modules II
[3]   On the decomposition numbers of the Hecke algebra of G(m,1,n) [J].
Ariki, S .
JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 1996, 36 (04) :789-808
[4]   Cluster algebras III: Upper bounds and double Bruhat cells [J].
Berenstein, A ;
Fomin, S ;
Zelevinsky, A .
DUKE MATHEMATICAL JOURNAL, 2005, 126 (01) :1-52
[5]   Cluster structures for 2-Calabi-Yau categories and unipotent groups [J].
Buan, A. B. ;
Iyama, O. ;
Reiten, I. ;
Scott, J. .
COMPOSITIO MATHEMATICA, 2009, 145 (04) :1035-1079
[6]   Tilting theory and cluster combinatorics [J].
Buan, Aslak Bakke ;
Marsh, Bethany Rose ;
Reineke, Markus ;
Reiten, Idun ;
Todorov, Gordana .
ADVANCES IN MATHEMATICS, 2006, 204 (02) :572-618
[7]   From triangulated categories to cluster algebras [J].
Caldero, Philippe ;
Keller, Bernhard .
INVENTIONES MATHEMATICAE, 2008, 172 (01) :169-211
[8]   Cluster algebras as Hall algebras of quiver representations [J].
Caldero, Philippe ;
Chapoton, Frederic .
COMMENTARII MATHEMATICI HELVETICI, 2006, 81 (03) :595-616
[9]   QUANTUM AFFINE ALGEBRAS [J].
CHARI, V ;
PRESSLEY, A .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1991, 142 (02) :261-283
[10]  
Chari V., 1995, REPRESENTATIONS GROU, P59