The character of the total power operation

Abstract

In this paper we compute the total power operation for the Morava $E$-theory of any finite group up to torsion. Our formula is stated in terms of the $G{L}_n(Q_p)$-action on the Drinfeld ring of full level structures on the formal group associated to $E$-theory. It can be specialized to give explicit descriptions of many classical operations. Moreover, we show that the character map of Hopkins, Kuhn, and Ravenel from $E$-theory to $G{L}_n(Z_p)$-invariant generalized class functions is a natural transformation of global power functors on finite groups.

Minor revisions, fixes, added some examples

References in corpus (4)

• Power operations for Morava E-theory of height 2 at the prime 2
• Global Mackey functors with operations and n-special lambda rings
• Centralizers in good groups are good
• On the Morava $E$-theory of wreath products of symmetric groups

Cited by in corpus (3)

• A model for complex analytic equivariant elliptic cohomology from quantum field theory
• Power operations in the Stolz--Teichner program
• Universal Finite Subgroup of the Tate Curve