Character formulas for the operad of two compatible brackets and for the bi-Hamiltonian operad

V. V. Dotsenko; A. S. Khoroshkin

doi:10.1007/s10688-007-0001-3

Character formulas for the operad of two compatible brackets and for the bi-Hamiltonian operad

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1-17
Number of pages	17
Journal	Functional Analysis and its Applications
Volume	41
Issue number	1
DOIs	https://doi.org/10.1007/s10688-007-0001-3
State	Published - Jan 2007
Externally published	Yes

Bibliographical note

Funding Information:
∗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.

Keywords

Cohen-Macaulay poset
Compatible Poisson brackets
Distributive law
Koszul operad

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1007/s10688-007-0001-3

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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.",

keywords = "Cohen-Macaulay poset, Compatible Poisson brackets, Distributive law, Koszul operad",

author = "Dotsenko, {V. V.} and Khoroshkin, {A. S.}",

note = "Funding Information: ∗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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AU - Dotsenko, V. V.

AU - Khoroshkin, A. S.

N1 - Funding Information: ∗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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N2 - 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.

AB - 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.

KW - Cohen-Macaulay poset

KW - Compatible Poisson brackets

KW - Distributive law

KW - Koszul operad

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DO - 10.1007/s10688-007-0001-3

M3 - Article

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EP - 17

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

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ER -

Character formulas for the operad of two compatible brackets and for the bi-Hamiltonian operad

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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