The Lubin–Tate theory of configuration spaces: I

Abstract We construct a spectral sequence converging to the Lubin–Tate theory, that is, Morava ‐theory, of unordered configuration spaces and identify its ‐page as the homology of a Chevalley–Eilenberg‐like complex for Hecke Lie algebras. Based on this, we compute the ‐theory of the weight summands of iterated loop spaces of spheres (parametrising the weight operations on ‐algebras), as well as the ‐theory of the configuration spaces of points on a punctured surface. We read off the corresponding Morava ‐theory groups, which appear in a conjecture by Ravenel. Finally, we compute the ‐homology of the space of unordered configurations of particles on a punctured surface.