Peak algebra idempotents for Sn generate representations isomorphic to cohomology of Conf_n(RP^2 times R), and these peak representations decompose as sums of Thrall's higher Lie characters with fixed numbers of odd parts.
Arnol’d, Vladimir
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Configuration spaces and peak representations
Peak algebra idempotents for Sn generate representations isomorphic to cohomology of Conf_n(RP^2 times R), and these peak representations decompose as sums of Thrall's higher Lie characters with fixed numbers of odd parts.