Remarks on critical points of phase functions and norms of Bethe vectors
Representation Theory
2007-05-23 v1 Mathematical Physics
math.MP
Abstract
We consider a tensor product of a Verma module and the linear representation of . 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.
Keywords
Cite
@article{arxiv.math/9810087,
title = {Remarks on critical points of phase functions and norms of Bethe vectors},
author = {Evgeny Mukhin and Alexander Varchenko},
journal= {arXiv preprint arXiv:math/9810087},
year = {2007}
}