Subgroups of p-divisible groups and centralizers in symmetric groups

We give a formula relating the transfer maps for the cohomology theories E_n and C_t to the transchromatic generalized character maps of a previous paper by the author. We then apply this to understand the effect of the transchromatic generalized character maps on Strickland’s isomorphism between the Morava E-theory of the symmetric group Σ_p^k (modulo a transfer ideal) and the global sections of the scheme that classifies subgroups of order p^k in the formal group associated to E_n. This provides an algebro-geometric interpretation to the C_t-cohomology of the class of groups arising as centralizers of finite sets of commuting elements in symmetric groups.