Representation type of finite quiver Hecke algebras of type A2l(2)

JOURNAL OF ALGEBRA

卷:397

Article

Ariki, Susumu¹  Park, Euiyong² 

[1] Osaka Univ, Grad Sch Informat Sci & Technol, Dept Pure & Appl Math, Toyonaka, Osaka 5600043, Japan

[2] Univ Seoul, Dept Math, Seoul 130743, South Korea

关键词: Representation theory;    Quiver Hecke algebras;    Representation type;    Shifted Young diagrams;   

DOI  :  10.1016/j.jalgebra.2013.09.005

来源: Elsevier

【 摘 要 】

We study cyclotomic quiver Hecke algebras R-Lambda 0(beta) in type A(2l)((2)), where Lambda(0) is the fundamental weight. The algebras are natural A(2l)((2))-type analogue of Iwahori Hecke algebras associated with the symmetric group, from the viewpoint of the Fock space theory developed by the first author and his collaborators. We give a formula for the dimension of the algebra, and a simple criterion to tell the representation type. The criterion is a natural generalization of Erdmann and Nakano's for the lwahori-Hecke algebras. Except for the examples coming from cyclotomic Hecke algebras, no results of these kind existed for cyclotomic quiver Hecke algebras, and our results are the first instances beyond the case of cyclotomic Hecke algebras. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free