Asymptotic Solutions to the Knizhnik-Zamolodchikov Equation and Crystal Base

Abstract

The Knizhnik-Zamolodchikov equation associated with $s{\ell }_2$ 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 group $U_{q}s{\ell }_2$ is established, in particular, a correspondence between the Bethe vectors of the Gaudin model of an inhomogenious magnetic chain and the $\mathbb{Q}-$basis of the crystal base.

43 pages, amstex