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We show that the algebra of commuting Hamiltonians of the homogeneous  Heisenberg model has simple spectrum on the subspace of singular vectors of the tensor product of two-dimensional  -modules. As a byproduct we show that there exist exactly  two-dimensional vector subspaces  with a basis  such that deg  = , deg  =  −  + 1 and  ()( − 1) −  ( − 1)() = ( + 1).

Bethe Algebra of Homogeneous XXX Heisenberg Model has Simple Spectrum