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The action of S_n on the cohomology of M_{0,n}(R)

Eric M. Rains
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Abstract

In recent work (math/0507514) by Etingof, Henriques, Kamnitzer, and the author, a presentation and explicit basis was given for the rational cohomology of the real locus $\bar{M_{0,n}}(\RR)$ of the moduli space of stable genus 0 curves with $n$ marked points. We determine the graded character of the action of $S_n$ on this space (induced by permutations of the marked points), both in the form of a plethystic formula for the cycle index, and as an explicit product formula for the value of the character on a given cycle type.

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Eric M. Rains. 2006-06-14. The action of S_n on the cohomology of M_{0,n}(R). https://arxiv.org/abs/math/0601573

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