论文题目：Representation type of cyclotomic quiver Hecke algebras of type $A_\ell^{(1)}$

论文作者：Susumu Ariki，Linliang Song，Qi Wang

发表刊物：Advances in Mathematics

成果介绍：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 $A^{(1)}_\ell$ form a one-parameter family and cyclotomic Hecke algebras occur at a special parameter, i.e., $t=-2$ if $\ell=1$ and $t=(-1)^{\ell+1}$ if $\ell\geq2$.

所属学科：基础数学

论文地址：https://doi.org/10.1016/j.aim.2023.109329