Abstract
We consider the free 2-nilpotent graded Lie algebra \(\mathfrak{g}\) generated in degree one by a finite dimensional vector space V. We recall the beautiful result that the cohomology \(H^ \cdot \left( {\mathfrak{g},\mathbb{K}} \right)\) of \(\mathfrak{g}\) with trivial coefficients carries a GL(V)-representation having only the Schur modules V with self-dual Young diagrams {λ: λ = λ′} in its decomposition into GL(V)-irreducibles (each with multiplicity one). The homotopy transfer theorem due to Tornike Kadeishvili allows to equip the cohomology of the Lie algebra g with a structure of homotopy commutative algebra.
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Dubois-Violette, M., Popov, T. Homotopy transfer and self-dual Schur modules. Phys. Part. Nuclei 43, 708–710 (2012). https://doi.org/10.1134/S1063779612050115
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DOI: https://doi.org/10.1134/S1063779612050115