Norms of Eigenfunctions of Trigonometric KZB Operators.

Let be a simple Lie algebra and V [0]=V1⊗⋯⊗Vn[0] be the zero weight subspace of a tensor product of -modules. The trigonometric KZB operators are commuting differential operators acting on V [0]-valued functions on the Cartan subalgebra of . Meromorphic eigenfunctions of the operators are constructed by the Bethe ansatz. We introduce a symmetric bilinear form 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. [ABSTRACT FROM AUTHOR]