  I examine the Generalized K$\ddot{a}$hler geometry of classical $N=(2,2)$
superconformal WZW model on a compact group and relate the right-moving and
left-moving Kac-Moody superalgebra currents to the Generalized K$\ddot{a}$hler
geometry data using Hamiltonian formalism. It is shown that canonical Poisson
homogeneous space structure induced by the Generalized K$\ddot{a}$hler geometry
of the group manifold is crucial to provide $N=(2,2)$ superconformal
sigma-model with the Kac-Moody superalgebra symmetries. Biholomorphic gerbe
geometry is used to prove that Kac-Moody superalgebra currents are globally
defined.
