Crystals arising from the WKB analysis

This talk gives an introduction to the Stokes phenomenon of an irregular Knizhnik–Zamolodchikov equation, associated to a representation $L(\lambda)$ of ${\mathfrak gl}_n$. It then proves that the Stokes matrices of the equation produce representations of quantum group $U_q({\mathfrak gl}_n)$ on $L(\lambda)$. Motivated by the relation with quantum group, it further gives a realization of the gl_n-crystal structures on $L(\lambda)$ via the WKB approximation of the Stokes matrice.