91 citations · 871 across the 69 of their papers we have counts for
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On separation of variables and completeness of the Bethe ansatz for quantum gl_N Gaudin model
E. Mukhin, V. Tarasov, A. Varchenko
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-…
Schubert calculus and representations of general linear group
E. Mukhin, V. Tarasov, A. Varchenko
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 intersectio…
On reality property of Wronski maps
E. Mukhin, V. Tarasov, A. Varchenko
We prove that if all roots of the discrete Wronskian with step 1 of a set of quasi-exponentials with real bases are real, simple and differ by at least 1, then the complex span of…
Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel
Evgeny Mukhin, Vitaly Tarasov, Alexander Varchenko
Let be the tensor product of finite-dimensional polynomial evaluation Yangian -modules. Consider the universal difference operator $D = \sum_{k=0}^N (-1)^k T_k(u) e^{-…
Combinatorial Formulae for Nested Bethe Vectors
Vitaly Tarasov, Alexander Varchenko
We give combinatorial formulae for vector-valued weight functions (off-shell nested Bethe vectors) for tensor products of irreducible evaluation modules over the Yangian $Y({\mathf…