International Journal of Modern Physics B c ○ World Scientific Publishing Company Comments on the Deformed WN Algebra ∗

We obtain an explicit expression for the defining relation of the deformed WN algebra, DWA(ŝlN)q,t. Using this expression we can show that, in the q → 1 limit, DWA(ŝlN)q,t with t = e 2πi N q k+N N reduces to the slN -version of the Lepowsky-Wilson’s Z-algebra of level k, ZA(ŝlN)k . In other words DWA(ŝlN)q,t with t = e − 2πi N q k+N N can be considered as a q-deformation of ZA(ŝlN)k . In the appendix given by H. Awata, S. Odake and J. Shiraishi, we present an interesting relation between DWA(ŝlN)q,t and ζ-function regularization.