Norms of eigenfunctions to trigonometric KZB operators

Details Norms of eigenfunctions to trigonometric KZB operators Norms of eigenfunctions to trigonometric KZB operators

2010-10-03

arxiv.org/abs/1010.0447v2

Mathematics

Quantum Algebra

Latex, 29 pages, Sections extended, sections 7, 8 added

Scientific paper

Let $g$ be a simple Lie algebra and $V[0]=V_1\otimes...\otimes V_n[0]$ 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.

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