The Maximality of Certain Commutative Subalgebras in Yangians

详细

It is proved that any Bethe subalgebra corresponding to a regular semisimple element in a Yangian is a maximal commutative subalgebra and, moreover, the centralizer of its quadratic part. As a consequence, a description of such subalgebras as the traces of the R-matrix over all finite-dimensional representations of the Yangian is obtained.