  We study solutions of the Bethe Ansatz equation related to the trigonometric
Gaudin model associated to a simple Lie algebra g and a tensor product of
irreducible finite-dimensional representations. Having one solution, we
describe a construction of new solutions. The collection of all solutions
obtained from a given one is called a population. We show that the Weyl group
of g acts on the points of a population freely and transitively (under certain
conditions).
  To a solution of the Bethe Ansatz equation, one assigns a common eigenvector
(called the Bethe vector) of the trigonometric Gaudin operators. The dynamical
Weyl group projectively acts on the common eigenvectors of the trigonometric
Gaudin operators. We conjecture that this action preserves the set of Bethe
vectors and coincides with the action induced by the action on points of
populations. We prove the conjecture for sl_2.
