Poincare-Birkhoff-Witt expansions of the canonical elliptic differential form

Original · EN

We study the canonical U()-valued elliptic differential form, whose projections to different Kac-Moody algebras are key ingredients of the hypergeometric integral solutions of elliptic KZ differential equations and Bethe ansatz constructions. We explicitly determine the coefficients of the projections in the simple Lie algebras Aᵣ, Bᵣ, Cᵣ, Dᵣ in a conveniently chosen Poincare-Birkhoff-Witt basis. As an application we give a new formula for eigenfunctions of Hamiltonians of the Calogero-Moser model.