Mathematics – Quantum Algebra
Scientific paper
2007-06-05
Mathematics
Quantum Algebra
latex, 39 pages
Scientific paper
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 $gl_2$-modules. As a byproduct we show that there exist exactly $\binom {n}{l}-\binom{n}{l-1}$ two-dimensional vector subspaces $V \subset \C[u]$ with a basis $f,g\in V$ such that $\deg f = l, \deg g = n-l+1$ and $f(u)g(u-1) - f(u-1)g(u) = (u+1)^n$.
Mukhin Evgeny
Tarasov Vitaly
Varchenko Alexander
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