Character formulas for the operad of two compatible brackets and for the bihamiltonian operad

Abstract

We compute dimensions of the components for the operad of two compatible brackets and for the bihamiltonian operad. We also obtain character formulas for the representations of the symmetric groups and the $S{L}_2$ group in these spaces.

24 pages, accepted by Functional Analysis and its Applications, a few typos corrected

References in corpus (5)

• Vanishing theorems and character formulas for the Hilbert scheme of points in the plane
• Homology of generalized partition posets
• Koszul duality of operads and homology of partition posets
• Quadratic algebras related to the bihamiltonian operad
• Distributive Laws and the Koszulness

Cited by in corpus (14)

• Gröbner bases for operads
• Operads of compatible structures and weighted partitions
• Quadratic algebras related to the bihamiltonian operad
• Compatible associative products and trees
• Totally compatible associative and Lie dialgebras, tridendriform algebras and PostLie algebras
• Maurer-Cartan characterizations and cohomologies of compatible Lie algebras
• An effective criterion for Nielsen-Schreier varieties
• Wheeled props in algebra, geometry and quantization
• Cohomology and deformations of compatible Hom-Lie algebras
• Matching Rota-Baxter algebras, matching dendriform algebras and matching pre-Lie algebras
• A classification of nilpotent compatible Lie algebras
• Universal enveloping algebra of a pair of compatible Lie brackets
• Prop profile of bi-Hamiltonian structures
• Combinatorial bases for multilinear parts of free algebras with double compatible brackets