Bethe Algebra of Homogeneous XXX Heisenberg Model Has Simple Spectrum

2007/06/05 by Mukhin, E., Tarasov, V., Varchenko, A.
#Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.0706.0688

Abstract

We show that the algebra of commuting Hamiltonians of the homogeneous XXX Heisenberg model has simple spectrum on the subspace of singular vectors of the tensor product of two-dimensional gl₂-modules. As a byproduct we show that there exist exactly \binom nl-\binomnl-1 two-dimensional vector subspaces V ⊂ \C[u] with a basis f,g∈ V such that °f = l, °g = n-l+1 and f(u)g(u-1) - f(u-1)g(u) = (u+1)ⁿ.

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