Abstract
An explicit formula is given for the graded trace of a permutation acting on the cohomology of the space of configurations of n ordered distinct points of R d. This is applied to determine the top and total cohomology as modules for the symmetric group, and to locate the occurrence of the alternating representation.
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Lehrer, G.I. Equivariant Cohomology of Configurations in Rd . Algebras and Representation Theory 3, 377–384 (2000). https://doi.org/10.1023/A:1009906210797
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DOI: https://doi.org/10.1023/A:1009906210797