Categorification of highest weight modules via Khovanov-Lauda-Rouquier algebras

被引：79

作者：

Kang, Seok-Jin ^{[1
,2
]}

Kashiwara, Masaki ^{[1
,3
]}

机构：

[1] Seoul Natl Univ, Dept Math Sci, Seoul 151747, South Korea

[2] Seoul Natl Univ, Res Inst Math, Seoul 151747, South Korea

[3] Kyoto Univ, Math Sci Res Inst, Kyoto 6068502, Japan

来源：

INVENTIONES MATHEMATICAE | 2012年 / 190卷 / 03期

基金：

日本学术振兴会;

关键词：

BASES;

D O I：

10.1007/s00222-012-0388-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove Khovanov-Lauda's cyclotomic categorification conjecture for all symmetrizable Kac-Moody algebras. Let be the quantum group associated with a symmetrizable Cartan datum and let V(I >) be the irreducible highest weight -module with a dominant integral highest weight I >. We prove that the cyclotomic Khovanov-Lauda-Rouquier algebra R (I >) gives a categorification of V(I >).

引用

页码：699 / 742

页数：44

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