Two facts were discussed: a) the Shapovalov norm of a Bethe vector in the
Gaudin model is equal to the Hessian of the logarithm of the corresponding
master function at the corresponding isolated critical point, b) the
different Bethe vectors are orthogonal with respect to the Shapovalov
form. It was explained that these facts are corollaries of a general
Bethe ansatz type construction associated with an arbitrary arrangement of
hyperplanes.

Keywords:

Bethe Ansatz; Hyperplane Arrangements; Gaudin Model.

Lecture #10697

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