PreprintEigenvalues of Bethe vectors in the Gaudin modelA. I. Molev and E. E. MukhinAbstractA theorem of Feigin, Frenkel and Reshetikhin provides expressions for the eigenvalues of the higher Gaudin Hamiltonians on the Bethe vectors in terms of elements of the center of the affine vertex algebra at the critical level. In our recent work, explicit HarishChandra images of generators of the center were calculated in all classical types. We combine these results to calculate the eigenvalues of the higher Gaudin Hamiltonians on the Bethe vectors in an explicit form. The HarishChandra images can be interpreted as elements of classical \(W\)algebras. We provide a direct connection between the rings of \(q\)characters and classical \(W\)algebras by calculating classical limits of the corresponding screening operators. This paper is available as a pdf (180kB) file.
