  We construct a canonical isomorphism between the Bethe algebra acting on a
multiplicity space of a tensor product of evaluation gl_N[t]-modules and the
scheme-theoretic intersection of suitable Schubert varieties. Moreover, we
prove that the multiplicity space as a module over the Bethe algebra is
isomorphic to the coregular representation of the scheme-theoretic
intersection.
  In particular, this result implies the simplicity of the spectrum of the
Bethe algebra for real values of evaluation parameters and the transversality
of the intersection of the corresponding Schubert varieties.
