In this paper it is shown that inclusions inside the Segal-Wilson Grassmannian give rise to Darboux transformations between the solutions of the $\KP$ hierarchy corresponding to these planes. We present a closed form of the operators that procure the transformation and express them in the related geometric data. Further the associated transformation on the level of $\tau$-functions is given.

We give a new geometric model for the quantization of the 4-dimensional conical (nilpotent) adjoint orbit $\OR$ of $\SL(3,\R)$. The space of quantization is the space of holomorphic functions on ${\C}^2-\{0\})$ which are square integrable with respect to a signed measure defined by a Meijer $G$-function. We construct the quantization out a non-flat Kaehler structure on ${\C}^2-\{0\})$ (the universal cover of $\OR$) with Kaehler potential $\rho=|z|^4$.