| Let g be a simple Lie algebra and V[0] = V 1 ⊗&cdots;⊗ Vn[0] the zero weight subspace of a tensor product of g -modules. The trigonometric KZB operators are commuting differential operators acting on V[0]-valued functions on the Cartan subalgebra of g . Meromorphic eigenfunctions to the operators are constructed by the Bethe ansatz. We introduce a scalar product on a suitable space of functions such that the operators become symmetric, and the square of the norm of a Bethe eigenfunction equals the Hessian of the master function at the corresponding critical point. |
