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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.

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
Full Text: DOI arXiv
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