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1 results

  • Norm of a Bethe vector and the Hessian of the master function

  • Evgeny Mukhin, Alexander Varchenko
  • Journal:
    Compositio Mathematica / Volume 141 / Issue 4 / July 2005
    Published online by Cambridge University Press:
    21 June 2005, pp. 1012-1028
    Print publication:
    July 2005
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  • We show that the norm of a Bethe vector in the $sl_{r+1}$ Gaudin model is equal to the Hessian of the corresponding master function at the corresponding critical point. In particular the Bethe vectors corresponding to non-degenerate critical points are non-zero vectors. This result is a byproduct of functorial properties of Bethe vectors studied in this paper. As another byproduct of functoriality we show that the Bethe vectors form a basis in the tensor product of several copies of first and last fundamental $sl_{r+1}$-modules.