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A transchromatic proof of Strickland’s theorem. (English) Zbl 1373.55004
Summary: In [Topology 37, No. 4, 757–779 (1998; Zbl 0912.55012)], N. P. Strickland proved that the Morava $$E$$-theory of the symmetric group has an algebro-geometric interpretation after taking the quotient by a certain transfer ideal. This result has influenced most of the work on power operations in Morava $$E$$-theory and provides an important calculational tool. In this paper we give a new proof of this result as well as a generalization by using transchromatic character theory. The character maps are used to reduce Strickland’s result to representation theory.

##### MSC:
 55N20 Generalized (extraordinary) homology and cohomology theories in algebraic topology 20C15 Ordinary representations and characters 55N91 Equivariant homology and cohomology in algebraic topology 55P35 Loop spaces
##### Keywords:
Morava $$E$$-theory; chromatic homotopy; character theory
Full Text:
##### References:
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