V. V. Dotsenko, A. S. Khoroshkin, “Character Formulas for the Operad of Two Compatible Brackets and for the Bi-Hamiltonian Operad”, Funktsional. Anal. i Prilozhen., 2007, Volume 41, Issue 1,Pages <nobr>1

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Character Formulas for the Operad of Two Compatible Brackets and for the Bi-Hamiltonian Operad

V. V. Dotsenko^a, A. S. Khoroshkin^b

^a Independent University of Moscow
^b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)

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: compatible Poisson brackets, distributive law, Koszul operad, Cohen–Macaulay poset.

UDC: 512.57

Received: 01.11.2005

DOI: 10.4213/faa2851