Gaudin model and branched coverings of a sphere

The Gaudin model is a physical system originally introduced for descriptions of the interaction of several charged particles on a straight line. Her the quantum version consists of n commuting operators (Hamiltonians), depending on n pairwise different complex parameters and acting on tensor product of n representations of the Lie algebra sl_2. One of the tasks the Gaudin model - to diagonalize these operators and understand how they change joint spectrum when changing parameters. It turns out that the mapping the joint spectrum of Hamiltonians for a given set of parameters continues to the ramified covering overline {M_ {0, n + 1}}, - the Deligne compactification Mumford spaces of moduli of stable rational curves with n + 1 marked with a dot. The talk will tell you about the device of this cover. in the case when n = 3 and the base of the covering is the Riemann sphere. Everything the necessary definitions and information will be given in the course of the report.