PreprintSegalSugawara vectors for the Lie algebra of type \(G_2\)A. I. Molev, E. Ragoucy and N. RozhkovskayaAbstractExplicit formulas for SegalSugawara vectors associated with the simple Lie algebra \(\mathfrak{g}\) of type \(G_2\) are found by using computerassisted calculations. This leads to a direct proof of the FeiginFrenkel theorem describing the center of the corresponding affine vertex algebra at the critical level. As an application, we give an explicit solution of Vinberg's quantization problem by providing formulas for generators of maximal commutative subalgebras of \(U(\mathfrak{g})\). We also calculate the eigenvalues of the Hamiltonians on the Bethe vectors in the Gaudin model associated with \(\mathfrak{g}\). This paper is available as a pdf (376kB) file.
