Representation type of finite quiver Hecke algebras of type A^(2)_{2l}
Representation type of finite quiver Hecke algebras of type A^(2)_{2l}
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A^(2)_{2l} 型有限箭袋 Hecke 代数的表示类型
DOI：
10.1016/j.jalgebra.2013.09.005
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Euiyong Park
中科院分区：
文献类型：
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作者：
Susumu Ariki;Euiyong Park
我们研究了a2(2)型切环颤振Hecke代数R Λ 0 (β)，其中Λ 0是基本权值。从第一作者及其合作者发展的Fock空间理论的观点来看，这些代数是与对称群相关的Iwahori-Hecke代数的自然a2(2)型模拟。给出了代数维数的一个公式，并给出了表示类型的一个简单判据。该判据是Erdmann和Nakano对Iwahori-Hecke代数的自然推广。除了来自切环Hecke代数的例子外，没有这类结果存在于切环颤切Hecke代数中，我们的结果是第一个超越切环Hecke代数的例子。
We study cyclotomic quiver Hecke algebras R Λ 0 (β) in type A 2 ℓ (2), where Λ 0 is the fundamental weight. The algebras are natural A 2 ℓ (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 Nakanoʼs for the Iwahori–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.