A cluster algebra approach to q-characters of Kirillov-Reshetikhin modules

被引：55
|
作者：
Hernandez, D. [1 ]
Leclerc, B. [2 ,3 ,4 ]
机构：
[1] Univ Paris 07, Sorbonne Paris Cite, CNRS, Inst Math Jussieu Paris Rive Gauche UMR 7586, Bat Sophie Germain,Case 7012, F-75205 Paris 13, France
[2] Normandie Univ, Caen, France
[3] UNICAEN, LMNO, F-14032 Caen, France
[4] CNRS, UMR 6139, F-14032 Caen, France
来源：
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2016年 / 18卷 / 05期
基金：
欧洲研究理事会;
关键词：
Quantum affine algebra; cluster algebras; q-characters; Kirillov-Reshetikhin modules; geometric character formula; FINITE-DIMENSIONAL REPRESENTATIONS; QUIVER VARIETIES; MINIMAL AFFINIZATIONS; QUANTUM GROUPS; T-SYSTEMS; PERIODICITIES; POTENTIALS;
D O I：
10.4171/JEMS/609
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We describe a cluster algebra algorithm for calculating the q-characters of Kirillov-Reshetikhin modules for any untwisted quantum affine algebra U-q(g) over cap. This yields a geometric q-character formula for tensor products of Kirillov-Reshetikhin modules. When g is of type A, D, E, this formula extends Nakajima's formula for q-characters of standard modules in terms of homology of graded quiver varieties.
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页码：1113 / 1159
页数：47
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