Publication date:
7 September 2017
Source:Advances in Mathematics, Volume 317
Author(s): Susumu Ariki
We find representation type of the cyclotomic quiver Hecke algebras $R^{\mathrm{\Lambda }}(\beta )$ of level two in affine type A. In particular, we have determined representation type for all the block algebras of Hecke algebras of classical type (except for characteristic two in type D), which has not been known for a long time. As an application of this result, we prove that block algebras of finite representation type are Brauer tree algebras whose Brauer trees are straight lines without exceptional vertex if the Hecke algebras are of classical type in good characteristic. We conjecture that this statement should hold for Hecke algebras of exceptional type.