Abstract
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.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 41, No. 1, pp. 1–22, 2007
Original Russian Text Copyright © by V. V. Dotsenko and A. S. Khoroshkin
The research of the first author is supported by President of the Russian Federation grant no. NSh-2044.2003.2 and by INTAS grant no. 03-3350. The research of the second author is supported by RFBR grant no. 04-01-00637 and INTAS grant no. 03-3350.
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Dotsenko, V.V., Khoroshkin, A.S. Character formulas for the operad of two compatible brackets and for the bi-Hamiltonian operad. Funct Anal Its Appl 41, 1–17 (2007). https://doi.org/10.1007/s10688-007-0001-3
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DOI: https://doi.org/10.1007/s10688-007-0001-3