Crystal bases arising from Stokes phenomenon.

In this paper, we give a complex analysis origin of crystal bases in representation of $\frak{gl}_n$. In particular, we propose that the WKB approximation of Stokes matrices, of certain meromorphic differential equations associated to a representation, gives rise to a crystal base. We prove it in a special case, and show that the corresponding crystal base is canonically isomorphic to the Gelfand-Tsetlin basis.