Representation type of cyclotomic quiver Hecke algebras of type Al(1)

被引：1

作者：

Ariki, Susumu ^{[1
]}

Song, Linliang ^{[2
]}

Wang, Qi ^{[3
]}

机构：

[1] Osaka Univ, Grad Sch Informat Sci & Technol, Dept Pure & Appl Math, 1-5 Yamadaoka, Suita, Osaka 5650871, Japan

[2] Tongji Univ, Sch Math Sci, Shanghai 200092, Peoples R China

[3] Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China

来源：

ADVANCES IN MATHEMATICS | 2023年 / 434卷

关键词：

Dominant maximal weights; Ariki-Koike algebras; KLR algebras; Brauer graph algebras; Representation type; Derived equivalence; DECOMPOSITION NUMBERS; EQUIVALENCES; MODULES;

D O I：

10.1016/j.aim.2023.109329

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We first investigate a connected quiver consisting of all dominant maximal weights for an integrable highest weight module in affine type A. This quiver provides an efficient method to obtain all dominant maximal weights. Then, we completely determine the representation type of cyclotomic Khovanov-Lauda-Rouquier algebras of arbitrary level in affine type A, by using the quiver we construct. This result gives a complete classification for the representation type of blocks of cyclotomic Hecke algebras since cyclotomic KLR algebras of type A(l)((1)) form a one-parameter family and cyclotomic Hecke algebras occur at a special parameter, i.e., t =-2 if l = 1 and t =(-1)(l+1) if l >= 2. (c) 2023 Elsevier Inc. All rights reserved.

引用

页数：68

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