Abstract: The original Clifford theory is a general theory regarding the group algebras over a field K. The theory relates simple modules of two algebras via inductions and restrictions. Clifford theory was later generalized by Dade to the notion of the graded Clifford systems. We show that any algebra with a graded Clifford system is another special case of the quantum wreath product algebras, introduced recently in a joint work with Nakano and Xiang. I’ll speak on a Clifford-type theory for quantum wreath product algebras. As an application, it takes care of the Specht modules (and thus simples) over generalized Hu algebras, which can be thought as the Hecke algebras for the wreath product Σm ≀ Σd between symmetric groups. Such a Clifford theory is an essential step towards proving the Ginzburg-Guay-Opdam-Rouquier conjecture for complex reflection groups.
