Geodesic
Character Formulas for the Operad of Two Compatible Brackets and for the Bi-Hamiltonian Operad
Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 1, pp. 1-22

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We compute the dimensions of the components for the operad of two compatible brackets and for the bi-Hamiltonian operad. We also obtain character formulas for the representations of symmetric groups and $SL_2$ in these spaces.
Mots-clés : compatible Poisson brackets, Koszul operad
Keywords: distributive law, Cohen–Macaulay poset. 
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     title = {Character {Formulas} for the {Operad} of {Two} {Compatible} {Brackets} and for the {Bi-Hamiltonian} {Operad}},
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V. V. Dotsenko; A. S. Khoroshkin. Character Formulas for the Operad of Two Compatible Brackets and for the Bi-Hamiltonian Operad. Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 1, pp. 1-22. http://geodesic.mathdoc.fr/item/FAA_2007_41_1_a0/