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

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

2005-02-14

arxiv.org/abs/math/0502296v2

Mathematics

Representation Theory

A typo corrected

Scientific paper

We study the canonical U(\n)-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 A_r, B_r, C_r, D_r 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.

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