Let G, H, and K be finite groups. Let X be a subgroup of H x G, and Y be a subgroup of K x H. Let M be an RX-module, and N be an RY-module, where R is a commutative ring. I will state a Mackey formula for the tensor product over H of the (RH,RG)-bimodule obtained by inducing M to H x G, and the (RK,RH)-bimodule obtained by inducing N to K x H.
This formula may be well known (reference would be welcome, in this case !), but the proof I will expose is new, I believe : it is a special case of a more general construction of tensor product of modules over bisets.

(Organized by S.Bouc)

Want to be kept updated on upcoming events? Then Click Here to Subscribe to Our Newsletters!