  We canonically quantize the tau-functions for the birational Weyl group
action arising from a nilpotent Poisson algebra proposed by Noumi and Yamada.
We also construct the q-difference deformation of the canonical quantization of
the tau-functions. Using the translation functors for the symmetrizable
Kac-Moody algebras, we prove the regularity of the quantum tau-functions,
namely, we show that the quantum tau-functions are polynomials in dependent
variables.
