By the work of Fong-Srinivasan, we have canonical labellings of block algebras in finite reductive groups of type A and D in non-defining characteristic. (Here, we only think about their adjoint type.) Similarly, we have canonical labellings of block algebras. By the works of Rouquier, Chuang-Kessar, Turner and Hida-M, we have a nice unipotent block in type A which is Morita equivalent t\ o a block algebra of the normalizer of a certain Levi subgroup. We can find such blocks infinitely many in type A. Actually, this is a maximal family. In my talk I'll report this block as well as new blocks in type D and E that are Morita equivalent to blocks of the normalizers of certain Levi subgroups. Maybe, I'll talk about the connection between canonical bases in Fock spaces and blocks in type A and D respectively.