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Remarks on critical points of phase functions and norms of Bethe vectors

Evgeny Mukhin·Alexander Varchenko
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Abstract

We consider a tensor product of a Verma module and the linear representation of $sl(n+1)$. We prove that the corresponding phase function, which is used in the solutions of the KZ equation with values in the tensor product, has a unique critical point and show that the Hessian of the logarithm of the phase function at this critical point equals the Shapovalov norm of the corresponding Bethe vector.

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BibTeXRIS

Evgeny Mukhin, Alexander Varchenko. 1998-10-14. Remarks on critical points of phase functions and norms of Bethe vectors. https://arxiv.org/abs/math/9810087

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