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

Abstract

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 $A_{\ell }^{(1)}$ 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 $\ell \ge 2$.

62 pages, minor revision, published by Advances in Mathematics

References in corpus (4)

• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Graded decomposition numbers for cyclotomic Hecke algebras
• Blocks of cyclotomic Hecke algebras
• Derived equivalence classification of Brauer graph algebras

Cited by in corpus (1)

• Representation type of higher level cyclotomic quiver Hecke algebras in affine type C