Asymptotic solutions to the Knizhnik-Zamolodchikov equation and crystal base

The Knizhnik-Zamolodchikov equation associated withsl2 is considered. The transition functions between asymptotic solutions to the Knizhnik-Zamolodchikov equation are described. A connection between asymptotic solutions and the crystal base in the tensor product of modules over the quantum groupUqsl2 is established, in particular, a correspondence between the Bethe vectors of the Gaudin model of an inhomogeneous magnetic chain and the Q-basis of the crystal base.