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Character formulas for the operad of two compatible brackets and for the bi-Hamiltonian operad. (English. Russian original) Zbl 1145.18001
Funct. Anal. Appl. 41, No. 1, 1-17 (2007); translation from Funkts. Anal. Prilozh. 41, No. 1, 1-22 (2007).
This paper studies the operad of two compatible brackets and the bi-Hamiltonian operad. It starts with the concepts and preliminaries on related operads and their properties, including the Koszulness and Cohen-Macaulayness. Then the main theorem on characters is stated and proved, followed by discussions on monomial bases and decompositions. The proofs make use of the connections of Koszul operads with Cohen-Macaulay posets and with distributive lattices.
Reviewer: Li Guo (Newark)

18D50 Operads (MSC2010)
20C30 Representations of finite symmetric groups
05E25 Group actions on posets, etc. (MSC2000)
06A11 Algebraic aspects of posets
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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