Norms of eigenfunctions to trigonometric KZB operators

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Last Modified
  • March 21, 2019
Creator
  • Jensen, Erik Jeremy
    • Affiliation: College of Arts and Sciences, Department of Mathematics
Abstract
  • Let g be a simple Lie algebra and V[0] be 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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  • In Copyright
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  • "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Mathematics."
Advisor
  • Varchenko, Alexander
Degree granting institution
  • University of North Carolina at Chapel Hill
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Place of publication
  • Chapel Hill, NC
Access right
  • Open access
Date uploaded
  • March 18, 2013

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