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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 $f,gin V$ such that $deg f = l, deg g = n-l+1$ and $f(u)g(u-1) - f(u-1)g(u) = (u+1)^n$.
In this note, we discuss implications of the results obtained in [MTV4]. It was shown there that eigenvectors of the Bethe algebra of the quantum gl_N Gaudin model are in a one-to-one correspondence with Fuchsian differential operators with polynomia
We study solutions of the Bethe ansatz equations of the non-homogeneous periodic XXX model associated to super Yangian $mathrm Y(mathfrak{gl}_{m|n})$. To a solution we associate a rational difference operator $mathcal D$ and a superspace of rational
We interpret the GL_n equivariant cohomology of a partial flag variety of flags of length N in C^n as the Bethe algebra of a suitable gl_N[t] module associated with the tensor power (C^N)^{otimes n}.
To any 2x2-matrix K one assigns a commutative subalgebra B^{K}subset U(gl_2[t]) called a Bethe algebra. We describe relations between the Bethe algebras, associated with the zero matrix and a nilpotent matrix.
Let $frak{g}$ be a finite dimensional simple complex Lie algebra and $U=U_q(frak{g})$ the quantized enveloping algebra (in the sense of Jantzen) with $q$ being generic. In this paper, we show that the center $Z(U_q(frak{g}))$ of the quantum group $U_