Equivalent Blocks of Finite General Linear Groups in Non-describing Characteristic

J. Chuang, R. Kessar, and J. Rickard have proved Brouéʹs Abelian defect group conjecture for many symmetric groups. We adapt the ideas of Kessar and Chuang towards finite general linear groups (represented over non-describing characteristic). We then describe Morita equivalences between certain p-blocks of GLn(q) with defect group Cpα × Cpα, as q varies (see Theorem 2). Here p and q are coprime. This generalizes work of S. Koshitani and M. Hyoue, who proved the same result for principal blocks of GLn(q) when p = 3, α = 1, in a different