Orthogonality of Bethe Ansatz eigenfunctions for the Laplacian on a hyperoctahedral Weyl alcove

Abstract

We prove the orthogonality of the Bethe Ansatz eigenfunctions for the Laplacian on a hyperoctahedral Weyl alcove with repulsive homogeneous Robin boundary conditions at the walls. To this end these eigenfunctions are retrieved as the continuum limit of an orthogonal basis of algebraic Bethe Ansatz eigenfunctions for a finite $q$-boson system endowed with diagonal open-end boundary interactions.

48 pages, LaTeX

References in corpus (4)

• Trigonometric Cherednik algebra at critical level and quantum many-body problems
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• Boundary transfer matrices and boundary quantum KZ equations
• Branching Formula for Macdonald-Koornwinder Polynomials

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